// Numbas version: exam_results_page_options
{"name": "Straight lines: one point gradient", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Straight lines: one point gradient", "tags": ["graph", "linear", "linear equation", "Straight Line", "straight line", "y=mx+b"], "metadata": {"description": "<p>Given one point and the gradient determine the equation of the line.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-12..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "brise": {"name": "brise", "group": "Ungrouped variables", "definition": "-if(brun=2,random(1,3,5,7),if(brun=3,random(1,2,4,5,7),if(brun=5,random(1,2,3,4,6,7),if(brun=7,random(1,2,3,4,5,6),'er'))))", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(-5..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "rise": {"name": "rise", "group": "Ungrouped variables", "definition": "if(run=2,random(1,3,5,7),if(run=3,random(1,2,4,5,7),if(run=5,random(1,2,3,4,6,7),if(run=7,random(1,2,3,4,5,6),'er'))))", "description": "", "templateType": "anything", "can_override": false}, "brun": {"name": "brun", "group": "Ungrouped variables", "definition": "random(2,3,5,7)", "description": "", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "random(-1,1,2,-2)", "description": "", "templateType": "anything", "can_override": false}, "bpoint_y": {"name": "bpoint_y", "group": "Ungrouped variables", "definition": "bb+brise*bscale", "description": "", "templateType": "anything", "can_override": false}, "point_y": {"name": "point_y", "group": "Ungrouped variables", "definition": "b+rise*scale", "description": "", "templateType": "anything", "can_override": false}, "run": {"name": "run", "group": "Ungrouped variables", "definition": "random(2,3,5,7)", "description": "", "templateType": "anything", "can_override": false}, "bscale": {"name": "bscale", "group": "Ungrouped variables", "definition": "random(-2..2 except [0,scale])", "description": "", "templateType": "anything", "can_override": false}, "point_x": {"name": "point_x", "group": "Ungrouped variables", "definition": "run*scale", "description": "", "templateType": "anything", "can_override": false}, "bpoint_x": {"name": "bpoint_x", "group": "Ungrouped variables", "definition": "brun*bscale", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "run", "rise", "point_y", "point_x", "scale", "bb", "brun", "brise", "bscale", "bpoint_y", "bpoint_x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The gradient intercept form of the&nbsp;line that passes through the point ({point_x},{point_y}) with a gradient of $\\simplify{{rise}/{run}}$ is $y=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>There are two common ways to approach these questions:</p>\n<ol>\n<li>Use the one point gradient formula $y-y_1=m(x-x_1)$.&nbsp;Or,<br/><br/></li>\n<li>Substitute the $x$ and $y$ values of the point and the value for $m$ into the&nbsp;gradient intercept form of a line&nbsp;$y=mx+b$ to determine $b$. Now you have $m$ and $b$ so you can write the equation of the line in the form $y=mx+b$.</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose we had to find the equation of the line through $(2,3)$ with a gradient of $\\frac{1}{4}$. The following are examples of using the above approaches:</p>\n<ol>\n<li>Substitute $m=\\frac{1}{4}$ and&nbsp;$(x_1,y_1)=(2,3)$ into the equation&nbsp;$y-y_1=m(x-x_1)$. This gives $y-3=\\frac{1}{4}(x-2)$.&nbsp;Expanding the brackets we have $y-3=\\frac{x}{4}-\\frac{1}{2}$. Making $y$ the subject gives $y=\\frac{x}{4}+\\frac{5}{2}$.<br/><br/></li>\n<li>Take the point $(2,3)$ as&nbsp;$(x,y)$ and substitute this and the gradient into the equation $y=mx+b$. This gives $3=\\frac{1}{4}(2)+b$. Solving for $b$ gives $b=\\frac{5}{2}$. Therefore the equation of the line is $y=\\frac{x}{4}+\\frac{5}{2}$.</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<p>Recall $\\frac{x}{4}$ is the same as $\\frac{1}{4}x$.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{rise}/{run}*x+{b}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["="], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The gradient intercept form of the&nbsp;line that passes through the point ({bpoint_x},{bpoint_y}) with a gradient of $\\simplify{{brise}/{brun}}$ is $y=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>There are two common ways to approach these questions:</p>\n<ol>\n<li>Use the one point gradient formula $y-y_1=m(x-x_1)$.&nbsp;Or,<br/><br/></li>\n<li>Substitute the $x$ and $y$ values of the point and the value for $m$ into the&nbsp;gradient intercept form of a line&nbsp;$y=mx+b$ to determine $b$. Now you have $m$ and $b$ so you can write the equation of the line in the form $y=mx+b$.</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose we had to find the equation of the line through $(2,3)$ with a gradient of $-\\frac{1}{4}$. The following are examples of using the above approaches:</p>\n<ol>\n<li>Substitute $m=-\\frac{1}{4}$ and&nbsp;$(x_1,y_1)=(2,3)$ into the equation&nbsp;$y-y_1=m(x-x_1)$. This gives $y-3=-\\frac{1}{4}(x-2)$.&nbsp;Expanding the brackets we have $y-3=-\\frac{x}{4}+\\frac{1}{2}$. Making $y$ the subject gives $y=-\\frac{x}{4}+\\frac{7}{2}$.<br/><br/></li>\n<li>Take the point $(2,3)$ as&nbsp;$(x,y)$ and substitute this and the gradient into the equation $y=mx+b$. This gives $3=-\\frac{1}{4}(2)+b$. Solving for $b$ gives $b=\\frac{7}{2}$. Therefore the equation of the line is $y=-\\frac{x}{4}+\\frac{7}{2}$.</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<p>Recall $-\\frac{x}{4}$ is the same as $-\\frac{1}{4}x$.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{brise}/{brun}*x+{bb}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["="], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}