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{"feedback": {"showanswerstate": true, "showactualmark": true, "advicethreshold": 0, "intro": "<p>Today, you will be graphing linear functions.&nbsp; You will also be identifying key characteristics of them via their graph or equation.</p>", "feedbackmessages": [], "showtotalmark": true, "allowrevealanswer": true}, "metadata": {"description": "Plot linear functions and identify key characteristics.", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "navigation": {"browse": true, "startpassword": "", "onleave": {"action": "none", "message": ""}, "preventleave": true, "allowregen": true, "reverse": true, "showfrontpage": true, "allowsteps": true, "showresultspage": "oncompletion"}, "timing": {"timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}, "allowPause": true}, "showstudentname": true, "duration": 0, "showQuestionGroupNames": false, "percentPass": 0, "name": "NCM4 U1L1 PRACTICE Graphing Linear Functions", "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "NC Math 4 U1L1 Terry's copy of  Graphs I: Linear Coordinates", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"g": {"description": "<p>This is the x-coordinate of the fourth point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "g"}, "c": {"description": "<p>This is the x-coordinate of the second point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "c"}, "h": {"description": "<p>This is the y-coordinate of the fourth point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "h"}, "f": {"description": "<p>This is the y-coordinate of the third point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "f"}, "ee": {"description": "<p>This is the x-coordinate of the third point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "ee"}, "b": {"description": "<p>This is the y-coordinate of the first point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "b"}, "a": {"description": "<p>This is the x-coordinate of the first point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "a"}, "d": {"description": "<p>This is the y-coordinate of the second point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "d"}}, "advice": "<p>The correct answers are obtained as follows.</p>\n<ul>\n<li>The point $A$ is distance $\\var{a}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{a}$.</li>\n<li>The point $A$ is distance $\\var{b}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{b}$.</li>\n<li>The point $B$ is distance $\\var{c}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{c}$.</li>\n<li>The point $B$ is distance $\\var{d}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{d}$.</li>\n<li>The point $C$ is distance $\\var{ee}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{ee}$.</li>\n<li>The point $C$ is distance $\\var{f}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{f}$.</li>\n<li>The point $D$ is distance $\\var{g}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{g}$.</li>\n<li>The point $D$ is distance $\\var{h}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{h}$.</li>\n</ul>\n<p></p>", "functions": {"dragpoint": {"parameters": [], "language": "javascript", "type": "html", "definition": "// set up the board\nJXG.Options.point.showInfobox = false;\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-11,11,11,-11],grid:true,withLabel:true});\n\nvar board = div.board;\n\nvar x1 = Numbas.jme.unwrapValue(scope.variables.a);\nvar y1 = Numbas.jme.unwrapValue(scope.variables.b);\nvar x2 = Numbas.jme.unwrapValue(scope.variables.c);\nvar y2 = Numbas.jme.unwrapValue(scope.variables.d);\nvar x3 = Numbas.jme.unwrapValue(scope.variables.ee);\nvar y3 = Numbas.jme.unwrapValue(scope.variables.f);\nvar x4 = Numbas.jme.unwrapValue(scope.variables.g);\nvar y4 = Numbas.jme.unwrapValue(scope.variables.h);\n\nvar e = board.create('point',[10,0],{size:-1,name:'x'});\ne.setProperty({fixed:true});\nvar f = board.create('point',[0,10],{size:-1,name:'y'});\nf.setProperty({fixed:true});\n\nvar a = board.create('point',[x1,y1],{size:5});\na.setProperty({fixed:true});\nvar b = board.create('point',[x2,y2],{size:5});\nb.setProperty({fixed:true});\nvar c = board.create('point',[x3,y3],{size:5});\nc.setProperty({fixed:true});\nvar d = board.create('point',[x4,y4],{size:5});\nd.setProperty({fixed:true});\n\nreturn div;"}}, "rulesets": {}, "showQuestionGroupNames": false, "tags": [], "type": "question", "statement": "<p>What are the coordinates of the points $A$-$D$ on the following graph?</p>\n<p>Note that all coordinates are whole numbers.</p>\n<p>{dragpoint()}</p>", "ungrouped_variables": ["a", "b", "c", "d", "ee", "f", "g", "h"], "parts": [{"steps": [{"marks": 0, "prompt": "<p>Coordinates are given in the form&nbsp;$(x,y)$</p>\n<p>In order to find the coordinate of a certain point, you must first find the $x$ coordinate by looking at which value the point is on the x-axis (the horizontal axis). Then, find the $y$ coordinate by looking at which value the point is on the y-axis (the vertical axis).</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information", "variableReplacements": []}], "showCorrectAnswer": true, "marks": 0, "prompt": "<p>The coordinates of $A$ are&nbsp;$\\big($[[0]],[[1]]$\\big)$.</p>\n<p><span id=\"distance\">The coordinates of $B$ are&nbsp;$\\big($[[2]],[[3]]$\\big)$.</span></p>\n<p><span id=\"distance\">The coordinates of $C$ are&nbsp;$\\big($[[4]],[[5]]$\\big)$.</span></p>\n<p><span id=\"distance\">The coordinates of $D$ are $\\big($[[6]],[[7]]$\\big)$.</span></p>", "scripts": {}, "gaps": [{"maxValue": "a", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "a", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "b", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "b", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "c", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "c", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "d", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "d", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "ee", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "ee", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "f", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "f", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "g", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "g", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "h", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "h", "integerAnswer": true, "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "stepsPenalty": 0}], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "metadata": {"description": "<p>This question allows you to practice identifying the coordinates of points on graphs.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "variablesTest": {"condition": "c<>a and ee<>a and g<>a and ee<>c and g<>c and g<>ee", "maxRuns": 100}}, {"name": "NC Math 4 U1L1 Terry's copy of  Graphs I: Linear Coordinates", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"g": {"description": "<p>This is the x-coordinate of the fourth point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "g"}, "c": {"description": "<p>This is the x-coordinate of the second point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "c"}, "h": {"description": "<p>This is the y-coordinate of the fourth point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "h"}, "f": {"description": "<p>This is the y-coordinate of the third point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "f"}, "ee": {"description": "<p>This is the x-coordinate of the third point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "ee"}, "b": {"description": "<p>This is the y-coordinate of the first point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "b"}, "a": {"description": "<p>This is the x-coordinate of the first point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "a"}, "d": {"description": "<p>This is the y-coordinate of the second point.</p>", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10)", "name": "d"}}, "advice": "<p>The correct answers are obtained as follows.</p>\n<ul>\n<li>The point $A$ is distance $\\var{a}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{a}$.</li>\n<li>The point $A$ is distance $\\var{b}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{b}$.</li>\n<li>The point $B$ is distance $\\var{c}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{c}$.</li>\n<li>The point $B$ is distance $\\var{d}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{d}$.</li>\n<li>The point $C$ is distance $\\var{ee}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{ee}$.</li>\n<li>The point $C$ is distance $\\var{f}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{f}$.</li>\n<li>The point $D$ is distance $\\var{g}$ from the origin in the horizontal direction (positive is to the right and negative is to the left), so its $x$-coordinate is $\\var{g}$.</li>\n<li>The point $D$ is distance $\\var{h}$ from the origin in the vertical direction (positive is upwards and negative is downwards), so its $y$-coordinate is $\\var{h}$.</li>\n</ul>\n<p></p>", "functions": {"dragpoint": {"parameters": [], "language": "javascript", "type": "html", "definition": "// set up the board\nJXG.Options.point.showInfobox = false;\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-11,11,11,-11],grid:true,withLabel:true});\n\nvar board = div.board;\n\nvar x1 = Numbas.jme.unwrapValue(scope.variables.a);\nvar y1 = Numbas.jme.unwrapValue(scope.variables.b);\nvar x2 = Numbas.jme.unwrapValue(scope.variables.c);\nvar y2 = Numbas.jme.unwrapValue(scope.variables.d);\nvar x3 = Numbas.jme.unwrapValue(scope.variables.ee);\nvar y3 = Numbas.jme.unwrapValue(scope.variables.f);\nvar x4 = Numbas.jme.unwrapValue(scope.variables.g);\nvar y4 = Numbas.jme.unwrapValue(scope.variables.h);\n\nvar e = board.create('point',[10,0],{size:-1,name:'x'});\ne.setProperty({fixed:true});\nvar f = board.create('point',[0,10],{size:-1,name:'y'});\nf.setProperty({fixed:true});\n\nvar a = board.create('point',[x1,y1],{size:5});\na.setProperty({fixed:true});\nvar b = board.create('point',[x2,y2],{size:5});\nb.setProperty({fixed:true});\nvar c = board.create('point',[x3,y3],{size:5});\nc.setProperty({fixed:true});\nvar d = board.create('point',[x4,y4],{size:5});\nd.setProperty({fixed:true});\n\nreturn div;"}}, "rulesets": {}, "showQuestionGroupNames": false, "tags": [], "type": "question", "statement": "<p>What are the coordinates of the points $A$-$D$ on the following graph?</p>\n<p>Note that all coordinates are whole numbers.</p>\n<p>{dragpoint()}</p>", "ungrouped_variables": ["a", "b", "c", "d", "ee", "f", "g", "h"], "parts": [{"steps": [{"marks": 0, "prompt": "<p>Coordinates are given in the form&nbsp;$(x,y)$</p>\n<p>In order to find the coordinate of a certain point, you must first find the $x$ coordinate by looking at which value the point is on the x-axis (the horizontal axis). Then, find the $y$ coordinate by looking at which value the point is on the y-axis (the vertical axis).</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information", "variableReplacements": []}], "showCorrectAnswer": true, "marks": 0, "prompt": "<p>The coordinates of $A$ are&nbsp;$\\big($[[0]],[[1]]$\\big)$.</p>\n<p><span id=\"distance\">The coordinates of $B$ are&nbsp;$\\big($[[2]],[[3]]$\\big)$.</span></p>\n<p><span id=\"distance\">The coordinates of $C$ are&nbsp;$\\big($[[4]],[[5]]$\\big)$.</span></p>\n<p><span id=\"distance\">The coordinates of $D$ are $\\big($[[6]],[[7]]$\\big)$.</span></p>", "scripts": {}, "gaps": [{"maxValue": "a", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "a", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "b", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "b", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "c", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "c", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "d", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "d", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "ee", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "ee", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "f", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "f", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "g", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "g", "integerAnswer": true, "showCorrectAnswer": true}, {"maxValue": "h", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "integerPartialCredit": 0, "type": "numberentry", "variableReplacements": [], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "minValue": "h", "integerAnswer": true, "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "stepsPenalty": 0}], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "metadata": {"description": "<p>This question allows you to practice identifying the coordinates of points on graphs.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "variablesTest": {"condition": "c<>a and ee<>a and g<>a and ee<>c and g<>c and g<>ee", "maxRuns": 100}}, {"name": "NC Math 4 U1L1 Graphing Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "advice": "", "tags": [], "statement": "<p>You are given the equation&nbsp;$y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.&nbsp;</p>", "preamble": {"css": "", "js": ""}, "parts": [{"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>This equation, or its graph, can be described as a</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "distractors": ["", "", "", "", "", ""], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>straight line</p>", "<p>parabola/quadratic</p>", "<p>cubic</p>", "<p>hyperbola</p>", "<p>circle</p>", "<p>quartic</p>"], "shuffleChoices": true, "marks": 0, "matrix": ["1", "0", "0", 0, 0, 0], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>An equation of the form $y=ax+b$ is&nbsp;known as&nbsp;a linear equation,&nbsp;and its graph is a straight line.&nbsp;</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far left of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "lleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the left of the graph $x$ is negative, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&gt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&lt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far right&nbsp;of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "rleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the right&nbsp;of the graph $x$ is positive, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&lt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&gt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": true, "minValue": "{b}", "marks": 1, "maxValue": "{b}", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": true, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept is the value of $y$ when $x=0$, that is, the value of $y$ where the graph hits&nbsp;the $y$-axis. To find it, substitute $x=0$ into our equation:</p>\n<p>\\[y=\\simplify[unitFactor,basic,fractionNumbers]{{a}0+{b}}=\\var{b}.\\]</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept of the graph is $y=$[[0]].</p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"checkingType": "absdiff", "checkVariableNames": false, "valuegenerators": [], "useCustomName": false, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "unitTests": [], "showFeedbackIcon": true, "answer": "set({xints})", "scripts": {}, "failureRate": 1, "showPreview": true, "showCorrectAnswer": true, "marks": 1, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "jme", "customMarkingAlgorithm": ""}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p><em><strong>Round your decimal to three decimal places.</strong></em></p>\n<p>The $x$-intercept is the value of $x$ when $y=0$, that is, the value of $x$ where the graph hits&nbsp;the $x$-axis. To find it, substitute $y=0$ into our equation:</p>\n<p>\\[0=\\simplify[all,fractionNumbers]{{a}x+{b}} \\]</p>\n<p></p>\n<p>Solving this&nbsp;equation tells us that&nbsp;the $x$-intercept is $x=\\simplify[all, fractionNumbers]{{-b}/{a}}$.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The set of $x$-intercepts of the graph&nbsp;would be&nbsp;[[0]].</p>\n<p><strong>Note:&nbsp;</strong>If there are no intercepts, enter<strong> <strong>set()</strong></strong></p>\n<p><span>If there is only one intercept, say $x=5$, enter <strong><strong>set(5)</strong></strong></span></p>\n<p><span>If there are two intercepts, say $x=-2$ and $x=1.5$, enter <strong>set(-2,1.5)</strong></span></p>\n<p><span>If there are three intercepts, say $x=-2$,&nbsp;$x=1.5$ and $x=5$, enter<strong> <strong>set(-2,1.5,5)</strong></strong></span></p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": false, "minValue": "0", "marks": 1, "maxValue": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>A degree $n$ polynomial has at most $n-1$ bends in its graph.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>Given the degree of a polynomial is $1$, the maximum number of possible 'bends' or 'turns' in the graph is&nbsp;[[0]].</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}], "functions": {}, "ungrouped_variables": ["a", "b", "lleading", "rleading", "xints"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-6..6 except 0)"}, "b": {"name": "b", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-10..10)"}, "xints": {"name": "xints", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "precround(-b/a,3)"}, "lleading": {"name": "lleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a<0,1,0),if(a<0,0,1)]"}, "rleading": {"name": "rleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a>0,1,0),if(a>0,0,1)]"}}}, {"name": "NC Math 4 U1L1 Graphing Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "advice": "", "tags": [], "statement": "<p>You are given the equation&nbsp;$y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.&nbsp;</p>", "preamble": {"css": "", "js": ""}, "parts": [{"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>This equation, or its graph, can be described as a</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "distractors": ["", "", "", "", "", ""], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>straight line</p>", "<p>parabola/quadratic</p>", "<p>cubic</p>", "<p>hyperbola</p>", "<p>circle</p>", "<p>quartic</p>"], "shuffleChoices": true, "marks": 0, "matrix": ["1", "0", "0", 0, 0, 0], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>An equation of the form $y=ax+b$ is&nbsp;known as&nbsp;a linear equation,&nbsp;and its graph is a straight line.&nbsp;</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far left of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "lleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the left of the graph $x$ is negative, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&gt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&lt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far right&nbsp;of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "rleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the right&nbsp;of the graph $x$ is positive, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&lt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&gt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": true, "minValue": "{b}", "marks": 1, "maxValue": "{b}", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": true, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept is the value of $y$ when $x=0$, that is, the value of $y$ where the graph hits&nbsp;the $y$-axis. To find it, substitute $x=0$ into our equation:</p>\n<p>\\[y=\\simplify[unitFactor,basic,fractionNumbers]{{a}0+{b}}=\\var{b}.\\]</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept of the graph is $y=$[[0]].</p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"checkingType": "absdiff", "checkVariableNames": false, "valuegenerators": [], "useCustomName": false, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "unitTests": [], "showFeedbackIcon": true, "answer": "set({xints})", "scripts": {}, "failureRate": 1, "showPreview": true, "showCorrectAnswer": true, "marks": 1, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "jme", "customMarkingAlgorithm": ""}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p><em><strong>Round your decimal to three decimal places.</strong></em></p>\n<p>The $x$-intercept is the value of $x$ when $y=0$, that is, the value of $x$ where the graph hits&nbsp;the $x$-axis. To find it, substitute $y=0$ into our equation:</p>\n<p>\\[0=\\simplify[all,fractionNumbers]{{a}x+{b}} \\]</p>\n<p></p>\n<p>Solving this&nbsp;equation tells us that&nbsp;the $x$-intercept is $x=\\simplify[all, fractionNumbers]{{-b}/{a}}$.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The set of $x$-intercepts of the graph&nbsp;would be&nbsp;[[0]].</p>\n<p><strong>Note:&nbsp;</strong>If there are no intercepts, enter<strong> <strong>set()</strong></strong></p>\n<p><span>If there is only one intercept, say $x=5$, enter <strong><strong>set(5)</strong></strong></span></p>\n<p><span>If there are two intercepts, say $x=-2$ and $x=1.5$, enter <strong>set(-2,1.5)</strong></span></p>\n<p><span>If there are three intercepts, say $x=-2$,&nbsp;$x=1.5$ and $x=5$, enter<strong> <strong>set(-2,1.5,5)</strong></strong></span></p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": false, "minValue": "0", "marks": 1, "maxValue": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>A degree $n$ polynomial has at most $n-1$ bends in its graph.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>Given the degree of a polynomial is $1$, the maximum number of possible 'bends' or 'turns' in the graph is&nbsp;[[0]].</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}], "functions": {}, "ungrouped_variables": ["a", "b", "lleading", "rleading", "xints"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-6..6 except 0)"}, "b": {"name": "b", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-10..10)"}, "xints": {"name": "xints", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "precround(-b/a,3)"}, "lleading": {"name": "lleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a<0,1,0),if(a<0,0,1)]"}, "rleading": {"name": "rleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a>0,1,0),if(a>0,0,1)]"}}}, {"name": "NC Math 4 U1L1 Graphing Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "advice": "", "tags": [], "statement": "<p>You are given the equation&nbsp;$y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.&nbsp;</p>", "preamble": {"css": "", "js": ""}, "parts": [{"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>This equation, or its graph, can be described as a</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "distractors": ["", "", "", "", "", ""], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>straight line</p>", "<p>parabola/quadratic</p>", "<p>cubic</p>", "<p>hyperbola</p>", "<p>circle</p>", "<p>quartic</p>"], "shuffleChoices": true, "marks": 0, "matrix": ["1", "0", "0", 0, 0, 0], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>An equation of the form $y=ax+b$ is&nbsp;known as&nbsp;a linear equation,&nbsp;and its graph is a straight line.&nbsp;</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far left of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "lleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the left of the graph $x$ is negative, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&gt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&lt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "<p>As we move to the far right&nbsp;of the graph, the graph</p>", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["<p>goes upwards.</p>", "<p>goes downwards.</p>"], "shuffleChoices": false, "marks": 0, "matrix": "rleading", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What happens to the graph as you go far to the left or right is called the long term behaviour of a graph.</p>\n<p>The leading term (the term that includes the highest power) determines the long term behaviour of a&nbsp;polynomial. In our polynomial the leading term is&nbsp;$\\simplify[all,fractionNumbers]{{a}x}$.</p>\n<p>As we go far to the right&nbsp;of the graph $x$ is positive, and so $\\simplify[all,fractionNumbers]{{a}x}$&nbsp;<span data-jme-visible=\"a&lt;0\">is negative. That is, the graph goes downwards.</span>&nbsp;<span data-jme-visible=\"a&gt;0\">is positive. That is, the graph goes upwards.</span>&nbsp;</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": true, "minValue": "{b}", "marks": 1, "maxValue": "{b}", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": true, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept is the value of $y$ when $x=0$, that is, the value of $y$ where the graph hits&nbsp;the $y$-axis. To find it, substitute $x=0$ into our equation:</p>\n<p>\\[y=\\simplify[unitFactor,basic,fractionNumbers]{{a}0+{b}}=\\var{b}.\\]</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The $y$-intercept of the graph is $y=$[[0]].</p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"checkingType": "absdiff", "checkVariableNames": false, "valuegenerators": [], "useCustomName": false, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "unitTests": [], "showFeedbackIcon": true, "answer": "set({xints})", "scripts": {}, "failureRate": 1, "showPreview": true, "showCorrectAnswer": true, "marks": 1, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "jme", "customMarkingAlgorithm": ""}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p><em><strong>Round your decimal to three decimal places.</strong></em></p>\n<p>The $x$-intercept is the value of $x$ when $y=0$, that is, the value of $x$ where the graph hits&nbsp;the $x$-axis. To find it, substitute $y=0$ into our equation:</p>\n<p>\\[0=\\simplify[all,fractionNumbers]{{a}x+{b}} \\]</p>\n<p></p>\n<p>Solving this&nbsp;equation tells us that&nbsp;the $x$-intercept is $x=\\simplify[all, fractionNumbers]{{-b}/{a}}$.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>The set of $x$-intercepts of the graph&nbsp;would be&nbsp;[[0]].</p>\n<p><strong>Note:&nbsp;</strong>If there are no intercepts, enter<strong> <strong>set()</strong></strong></p>\n<p><span>If there is only one intercept, say $x=5$, enter <strong><strong>set(5)</strong></strong></span></p>\n<p><span>If there are two intercepts, say $x=-2$ and $x=1.5$, enter <strong>set(-2,1.5)</strong></span></p>\n<p><span>If there are three intercepts, say $x=-2$,&nbsp;$x=1.5$ and $x=5$, enter<strong> <strong>set(-2,1.5,5)</strong></strong></span></p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": false, "minValue": "0", "marks": 1, "maxValue": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>A degree $n$ polynomial has at most $n-1$ bends in its graph.</p>", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>Given the degree of a polynomial is $1$, the maximum number of possible 'bends' or 'turns' in the graph is&nbsp;[[0]].</p>\n<p></p>", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}], "functions": {}, "ungrouped_variables": ["a", "b", "lleading", "rleading", "xints"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-6..6 except 0)"}, "b": {"name": "b", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-10..10)"}, "xints": {"name": "xints", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "precround(-b/a,3)"}, "lleading": {"name": "lleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a<0,1,0),if(a<0,0,1)]"}, "rleading": {"name": "rleading", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[if(a>0,1,0),if(a>0,0,1)]"}}}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Slope-Intercept Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "statement": "<p>GIVEN:&nbsp; $\\simplify{y={m[1]}/{m[0]}x+{yint[1]}/{yint[0]}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"shuffleChoices": true, "customName": "", "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "distractors": ["", "", "", ""], "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', -yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yintSend], ['b', mSend]])}"], "minMarks": 0, "matrix": ["1", 0, 0, 0], "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "type": "1_n_2", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "B", "C", "m", "yint", "mSend", "yintSend"], "variables": {"yint": {"name": "yint", "description": "", "definition": "rational_approximation(C/B)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "rational_approximation(-A/B)", "templateType": "anything", "group": "Ungrouped variables"}, "mSend": {"name": "mSend", "description": "", "definition": "m[1]/m[0]", "templateType": "anything", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"name": "A", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "C": {"name": "C", "description": "", "definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables"}, "yintSend": {"name": "yintSend", "description": "", "definition": "yint[1]/yint[0]", "templateType": "anything", "group": "Ungrouped variables"}}, "functions": {}, "tags": [], "advice": "", "variable_groups": []}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Slope-Intercept Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "statement": "<p>GIVEN:&nbsp; $\\simplify{y={m[1]}/{m[0]}x+{yint[1]}/{yint[0]}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"shuffleChoices": true, "customName": "", "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "distractors": ["", "", "", ""], "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', -yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yintSend], ['b', mSend]])}"], "minMarks": 0, "matrix": ["1", 0, 0, 0], "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "type": "1_n_2", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "B", "C", "m", "yint", "mSend", "yintSend"], "variables": {"yint": {"name": "yint", "description": "", "definition": "rational_approximation(C/B)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "rational_approximation(-A/B)", "templateType": "anything", "group": "Ungrouped variables"}, "mSend": {"name": "mSend", "description": "", "definition": "m[1]/m[0]", "templateType": "anything", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"name": "A", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "C": {"name": "C", "description": "", "definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables"}, "yintSend": {"name": "yintSend", "description": "", "definition": "yint[1]/yint[0]", "templateType": "anything", "group": "Ungrouped variables"}}, "functions": {}, "tags": [], "advice": "", "variable_groups": []}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Slope-Intercept Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "statement": "<p>GIVEN:&nbsp; $\\simplify{y={m[1]}/{m[0]}x+{yint[1]}/{yint[0]}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"shuffleChoices": true, "customName": "", "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "distractors": ["", "", "", ""], "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', -yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yintSend], ['b', mSend]])}"], "minMarks": 0, "matrix": ["1", 0, 0, 0], "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "type": "1_n_2", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "B", "C", "m", "yint", "mSend", "yintSend"], "variables": {"yint": {"name": "yint", "description": "", "definition": "rational_approximation(C/B)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "rational_approximation(-A/B)", "templateType": "anything", "group": "Ungrouped variables"}, "mSend": {"name": "mSend", "description": "", "definition": "m[1]/m[0]", "templateType": "anything", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"name": "A", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "C": {"name": "C", "description": "", "definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables"}, "yintSend": {"name": "yintSend", "description": "", "definition": "yint[1]/yint[0]", "templateType": "anything", "group": "Ungrouped variables"}}, "functions": {}, "tags": [], "advice": "", "variable_groups": []}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Slope-Intercept Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "statement": "<p>GIVEN:&nbsp; $\\simplify{y={m[1]}/{m[0]}x+{yint[1]}/{yint[0]}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"shuffleChoices": true, "customName": "", "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "distractors": ["", "", "", ""], "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', -yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yintSend], ['b', mSend]])}"], "minMarks": 0, "matrix": ["1", 0, 0, 0], "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "type": "1_n_2", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "B", "C", "m", "yint", "mSend", "yintSend"], "variables": {"yint": {"name": "yint", "description": "", "definition": "rational_approximation(C/B)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "rational_approximation(-A/B)", "templateType": "anything", "group": "Ungrouped variables"}, "mSend": {"name": "mSend", "description": "", "definition": "m[1]/m[0]", "templateType": "anything", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"name": "A", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "C": {"name": "C", "description": "", "definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables"}, "yintSend": {"name": "yintSend", "description": "", "definition": "yint[1]/yint[0]", "templateType": "anything", "group": "Ungrouped variables"}}, "functions": {}, "tags": [], "advice": "", "variable_groups": []}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Slope-Intercept Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "statement": "<p>GIVEN:&nbsp; $\\simplify{y={m[1]}/{m[0]}x+{yint[1]}/{yint[0]}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"shuffleChoices": true, "customName": "", "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "distractors": ["", "", "", ""], "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-mSend], ['b', yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',mSend], ['b', -yintSend]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yintSend], ['b', mSend]])}"], "minMarks": 0, "matrix": ["1", 0, 0, 0], "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "type": "1_n_2", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["A", "B", "C", "m", "yint", "mSend", "yintSend"], "variables": {"yint": {"name": "yint", "description": "", "definition": "rational_approximation(C/B)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "rational_approximation(-A/B)", "templateType": "anything", "group": "Ungrouped variables"}, "mSend": {"name": "mSend", "description": "", "definition": "m[1]/m[0]", "templateType": "anything", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "A": {"name": "A", "description": "", "definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables"}, "C": {"name": "C", "description": "", "definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables"}, "yintSend": {"name": "yintSend", "description": "", "definition": "yint[1]/yint[0]", "templateType": "anything", "group": "Ungrouped variables"}}, "functions": {}, "tags": [], "advice": "", "variable_groups": []}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Standard Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "tags": [], "parts": [{"useCustomName": false, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', -yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yint], ['b', m]])}"], "showCorrectAnswer": true, "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "type": "1_n_2", "customName": "", "marks": 0, "shuffleChoices": true, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", ""], "matrix": ["1", 0, 0, 0], "variableReplacements": [], "minMarks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "showCellAnswerState": true, "maxMarks": 0, "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "unitTests": [], "customMarkingAlgorithm": ""}], "statement": "<p>GIVEN:&nbsp; $\\simplify{{A}x + {B}y={C}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "variables": {"m": {"name": "m", "templateType": "anything", "definition": "(-A/B)", "group": "Ungrouped variables", "description": ""}, "A": {"name": "A", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "yint": {"name": "yint", "templateType": "anything", "definition": "(C/B)", "group": "Ungrouped variables", "description": ""}, "C": {"name": "C", "templateType": "anything", "definition": "random(-10..10)", "group": "Ungrouped variables", "description": ""}, "B": {"name": "B", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "m", "yint"], "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {}, "advice": ""}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Standard Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "tags": [], "parts": [{"useCustomName": false, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', -yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yint], ['b', m]])}"], "showCorrectAnswer": true, "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "type": "1_n_2", "customName": "", "marks": 0, "shuffleChoices": true, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", ""], "matrix": ["1", 0, 0, 0], "variableReplacements": [], "minMarks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "showCellAnswerState": true, "maxMarks": 0, "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "unitTests": [], "customMarkingAlgorithm": ""}], "statement": "<p>GIVEN:&nbsp; $\\simplify{{A}x + {B}y={C}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "variables": {"m": {"name": "m", "templateType": "anything", "definition": "(-A/B)", "group": "Ungrouped variables", "description": ""}, "A": {"name": "A", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "yint": {"name": "yint", "templateType": "anything", "definition": "(C/B)", "group": "Ungrouped variables", "description": ""}, "C": {"name": "C", "templateType": "anything", "definition": "random(-10..10)", "group": "Ungrouped variables", "description": ""}, "B": {"name": "B", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "m", "yint"], "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {}, "advice": ""}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Standard Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "tags": [], "parts": [{"useCustomName": false, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', -yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yint], ['b', m]])}"], "showCorrectAnswer": true, "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "type": "1_n_2", "customName": "", "marks": 0, "shuffleChoices": true, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", ""], "matrix": ["1", 0, 0, 0], "variableReplacements": [], "minMarks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "showCellAnswerState": true, "maxMarks": 0, "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "unitTests": [], "customMarkingAlgorithm": ""}], "statement": "<p>GIVEN:&nbsp; $\\simplify{{A}x + {B}y={C}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "variables": {"m": {"name": "m", "templateType": "anything", "definition": "(-A/B)", "group": "Ungrouped variables", "description": ""}, "A": {"name": "A", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "yint": {"name": "yint", "templateType": "anything", "definition": "(C/B)", "group": "Ungrouped variables", "description": ""}, "C": {"name": "C", "templateType": "anything", "definition": "random(-10..10)", "group": "Ungrouped variables", "description": ""}, "B": {"name": "B", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "m", "yint"], "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {}, "advice": ""}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Standard Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "tags": [], "parts": [{"useCustomName": false, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', -yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yint], ['b', m]])}"], "showCorrectAnswer": true, "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "type": "1_n_2", "customName": "", "marks": 0, "shuffleChoices": true, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", ""], "matrix": ["1", 0, 0, 0], "variableReplacements": [], "minMarks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "showCellAnswerState": true, "maxMarks": 0, "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "unitTests": [], "customMarkingAlgorithm": ""}], "statement": "<p>GIVEN:&nbsp; $\\simplify{{A}x + {B}y={C}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "variables": {"m": {"name": "m", "templateType": "anything", "definition": "(-A/B)", "group": "Ungrouped variables", "description": ""}, "A": {"name": "A", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "yint": {"name": "yint", "templateType": "anything", "definition": "(C/B)", "group": "Ungrouped variables", "description": ""}, "C": {"name": "C", "templateType": "anything", "definition": "random(-10..10)", "group": "Ungrouped variables", "description": ""}, "B": {"name": "B", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "m", "yint"], "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {}, "advice": ""}, {"name": "NCM4 U1L1 Plot the graph of a linear equation Standard Form", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "tags": [], "parts": [{"useCustomName": false, "choices": ["{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',-m], ['b', yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',m], ['b', -yint]])}", "{geogebra_applet(\"https://www.geogebra.org/m/t2euxgf5\", [['m',yint], ['b', m]])}"], "showCorrectAnswer": true, "prompt": "<p>Select the plot that best represents the given linear equation.</p>", "type": "1_n_2", "customName": "", "marks": 0, "shuffleChoices": true, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", ""], "matrix": ["1", 0, 0, 0], "variableReplacements": [], "minMarks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "showCellAnswerState": true, "maxMarks": 0, "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "unitTests": [], "customMarkingAlgorithm": ""}], "statement": "<p>GIVEN:&nbsp; $\\simplify{{A}x + {B}y={C}}$</p>\n<p>FIND:&nbsp; Plot the equation of the line.</p>", "variables": {"m": {"name": "m", "templateType": "anything", "definition": "(-A/B)", "group": "Ungrouped variables", "description": ""}, "A": {"name": "A", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}, "yint": {"name": "yint", "templateType": "anything", "definition": "(C/B)", "group": "Ungrouped variables", "description": ""}, "C": {"name": "C", "templateType": "anything", "definition": "random(-10..10)", "group": "Ungrouped variables", "description": ""}, "B": {"name": "B", "templateType": "anything", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["A", "B", "C", "m", "yint"], "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {}, "advice": ""}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "extensions": ["geogebra", "jsxgraph"], "custom_part_types": [], "resources": []}