// Numbas version: exam_results_page_options
{"name": "Linear graphs: Reading gradient and intercept from an equation", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Linear graphs: Reading gradient and intercept from an equation", "tags": [], "metadata": {"description": "<p>Reading gradient and intercept from y=mx+c.</p>", "licence": "None specified"}, "statement": "<p>$y = \\simplify[fractionnumbers]{{m}x+{c}}$</p>", "advice": "<p>The equation is written in the form $y=mx+c$ where $m$ is the gradient and $c$ is the y-intercept.</p>\n<p>Since $y = \\simplify[fractionnumbers]{{m}x+{c}}$<br/>&nbsp; &nbsp; &nbsp; i.e. $= \\var[fractionnumbers]{m} \\times x + \\var{c}$ we can read that:</p>\n<p>$m=\\var[fractionnumbers]{m}$ and $c=\\var{c}$</p>\n<p>This is what the graph looks like:</p>\n<p>{app}</p>\n<p></p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n  800,500,\n  [\n    A: [\n      definition: p1,\n      label_visible: false,\n      visible: false\n    ],\n    B: [\n      definition: p2,\n      label_visible: false,\n      visible: false      \n    ],\n    line: [\n      definition: \"Line(A,B)\",\n      label_visible: false\n    ]\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(ay-by)/(ax-bx)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "ay-m*ax", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "vector(ax, ay)", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "vector(bx,by)", "description": "", "templateType": "anything", "can_override": false}, "uod": {"name": "uod", "group": "Ungrouped variables", "definition": "if(m=0,'horizontal',if(m=abs(m),'going up','going down'))", "description": "<p>if(m=abs(m),'positive','negative')</p>", "templateType": "anything", "can_override": false}, "ax": {"name": "ax", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ay": {"name": "ay", "group": "Ungrouped variables", "definition": "random(0,1,2,3)", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "Ungrouped variables", "definition": "random(ax+1..3) \n", "description": "", "templateType": "anything", "can_override": false}, "by": {"name": "by", "group": "Ungrouped variables", "definition": "random(0..4 except ay)\n", "description": "", "templateType": "anything", "can_override": false}, "app_advice": {"name": "app_advice", "group": "Ungrouped variables", "definition": "geogebra_applet(\n  800,500,\n  [\n    A: [\n      definition: p1,\n      label_visible: false,\n      visible: true\n    ],\n    B: [\n      definition: p2,\n      label_visible: false,\n      visible: true      \n    ],\n    \n    C: [\n      definition: p3,\n      label_visible: false,\n      visible: false      \n    ],\n    \n    line1: [\n      definition: \"Line(A,B)\",\n      label_visible: false,\n      visible: true\n    ],\n    \n    line2: [\n      definition: \"Segment(A,C)\",\n      label_visible: false,\n      visible: true\n    ],\n    \n   \n    \n    line3: [\n      definition: \"Segment(C,B)\",\n      label_visible: false,\n      visible: true\n    ]\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}, "p3": {"name": "p3", "group": "Ungrouped variables", "definition": "vector(bx,ay)", "description": "", "templateType": "anything", "can_override": false}, "pon": {"name": "pon", "group": "Ungrouped variables", "definition": "if(m=0,'zero',if(m=abs(m),'a positive number','a negative number'))", "description": "", "templateType": "anything", "can_override": false}, "sos": {"name": "sos", "group": "Ungrouped variables", "definition": "if(m=0,'horizontal',if(abs(m)<1,'shallow','steep'))", "description": "", "templateType": "anything", "can_override": false}, "mol": {"name": "mol", "group": "Ungrouped variables", "definition": "if(m=0,'zero',if(abs(m)<1,'less than 1','greater than or equal to 1'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "m<>1 OR c <> 0", "maxRuns": 100}, "ungrouped_variables": ["app", "m", "c", "P1", "P2", "uod", "ax", "ay", "bx", "by", "app_advice", "p3", "pon", "sos", "mol"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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>Does this line have a positive or negative gradient?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Positive", "Negative"], "matrix": ["if(m>0,1,0)", "if(m<0,1,0)"], "distractors": ["", ""]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the gradient of this line?</p>", "answer": "{m}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": "1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"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>What is the y-intercept of this line?</p>\n<p>This is the point where the function intersects the y-axis.&nbsp;</p>\n<p>(0,[[0]])</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c", "maxValue": "c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}