// Numbas version: finer_feedback_settings
{"name": "Graph a line from a word problem", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graph a line from a word problem", "tags": [], "metadata": {"description": "<p>Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.</p>\n<p>The line parameters and the given point are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A&nbsp;{job} charges \\$$\\var{callout}$ for a call out and \\$$\\var{rate}$ per hour for labour.</p>", "advice": "<p>An equation for the cost of hiring the plumber for $n$ hours is:</p>\n<p>$C = \\var{rate} n + \\var{callout}$</p>\n<p>For $\\var{n}$ hours, it will cost&nbsp; $C = \\var{rate} \\times \\var{n} + \\var{callout} =$ {costdollars}</p>\n<p>Your graph should look similar to this {geogebra_applet('https://www.geogebra.org/m/wxv4ykqj',defs)}</p>\n<p>Your graph needs:</p>\n<ul>\n<li>to&nbsp;start at (0,0).</li>\n<li>to show the line.</li>\n<li>to&nbsp;contain the point $(\\var{n},\\var{cost})$ and the point $(0,\\var{callout})$</li>\n<li>labels and arrows on both axes. In this graph, the horizontal axis is labelled $x$. However, you should have labelled yours as $n$ or $time (hours)$. In this graph, the vertical axis is labelled $y$. However, you should have labelled yours as $C$ or $Cost (\\$)$.</li>\n<li>a scale on each axis.</li>\n</ul>\n<p>You may have chosen different scales for your axes. This is fine.</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"callout": {"name": "callout", "group": "Ungrouped variables", "definition": "random(10..16)*5", "description": "", "templateType": "anything"}, "rate": {"name": "rate", "group": "Ungrouped variables", "definition": "random(10..24)*5", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(0.5,1,1.5,2,2.5,3,3.5,4)", "description": "<p>number of hours for which the plumber was hired.</p>", "templateType": "anything"}, "cost": {"name": "cost", "group": "Ungrouped variables", "definition": "callout + rate * n", "description": "<p>cost to hire the plumber for n hours</p>", "templateType": "anything"}, "costdollars": {"name": "costdollars", "group": "Ungrouped variables", "definition": "currency(cost,'$','')", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['a',rate],['b',callout],['xmin',0],['xmax',n*1.5],['ymin',0],['ymax',n*1.5*rate]\n  ]", "description": "", "templateType": "anything"}, "job": {"name": "job", "group": "Ungrouped variables", "definition": "random(\"plumber\",\"electrician\",\"handyman\",\"carpenter\",\"gardener\",\"tiler\",\"gutter installer\",\"stone mason\",\"glazier\",\"car mechanic\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["callout", "rate", "n", "cost", "costdollars", "defs", "job"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>Write down an equation to calculate the cost, $C$ of hiring the&nbsp;{job} for $h$ hours.</p>\n<p>Once you have completed the whole question, you can click on \"Reveal answers\" to check your equation.</p>"}, {"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, "prompt": "<p>How much would it cost to hire the&nbsp;{job} for $\\var{n}$ hours?</p>", "minValue": "cost", "maxValue": "cost", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Draw a graph showing the relationship between the number of hours the plumber spends on the job and the cost of the job.</p>\n<p>Once you are done, you can click on \"Reveal answers\" to see a sample graph.</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}