// Numbas version: finer_feedback_settings
{"name": "Transpose linear formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Transpose linear formula", "tags": [], "metadata": {"description": "<p>Rearrange a linear function in x and y to make y the subject. Line variables are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Transpose the formula \\(\\simplify{{selected_formula}}\\) to make \\(\\var{selected_variable}\\) the subject.</p>", "advice": "<p><span data-jme-visible=\"sel_formula=0 and sel_variable=1\">$\\begin{align}\\var{simplify(expression(a+\"x+\"+b+\"y\"),[\"basic\",\"unitFactor\"])}&amp;=\\var{c}\\\\ \\var{b}y&amp;=\\var{simplify(expression(c+\"-\"+a+\"x\"),[\"basic\",\"unitFactor\"])}\\qquad\\textrm{move }\\var{a}x\\textrm{ to the right}\\\\ y&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+b+\"-\"+a+\"/\"+b+\"x\"),[\"basic\",\"unitFactor\",\"unitDenominator\"])}\\qquad\\textrm{Divide by }\\var{b}\\\\y&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+b+\"-\"+a+\"/\"+b+\"x\"),\"all\")}\\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_formula=0 and sel_variable=0\">$\\begin{align}\\var{simplify(expression(a+\"x+\"+b+\"y\"),[\"basic\",\"unitFactor\"])}&amp;=\\var{c}\\\\ \\var{a}x &amp;= \\var{simplify(expression(c+\"-\"+b+\"y\"),[\"basic\",\"unitFactor\"])}\\qquad\\textrm{move }\\var{b}y\\textrm{ to the right}\\\\ x&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+a+\"-\"+b+\"/\"+a+\"y\"),[\"basic\",\"unitFactor\",\"unitDenominator\"])}\\qquad\\textrm{Divide by }\\var{a}\\\\x&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+a+\"-\"+b+\"/\"+a+\"y\"),[\"all\"])}\\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_formula=1 and sel_variable=1\">$\\begin{align}\\var{simplify(expression(a+\"x+\"+b+\"y-\"+c),[\"basic\",\"unitFactor\"])}&amp;=0\\\\ \\var{simplify(expression(a+\"x+\"+b+\"y\"),[\"basic\",\"unitFactor\"])}&amp;=\\var{c}\\qquad\\textrm{move }\\var{c}\\\\ \\var{b}y&amp;=\\var{simplify(expression(c+\"-\"+a+\"x\"),[\"basic\",\"unitFactor\"])}\\qquad\\textrm{move }\\var{a}x\\textrm{ to the right}\\\\ y&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+b+\"-\"+a+\"/\"+b+\"x\"),[\"basic\",\"unitFactor\",\"unitDenominator\"])}\\qquad\\textrm{Divide by }\\var{b}\\\\y&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+b+\"-\"+a+\"/\"+b+\"x\"),\"all\")}\\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_formula=1 and sel_variable=0\">$\\begin{align}\\var{simplify(expression(a+\"x+\"+b+\"y-\"+c),[\"basic\",\"unitFactor\"])}&amp;=0\\\\ \\var{simplify(expression(a+\"x+\"+b+\"y\"),[\"basic\",\"unitFactor\"])}&amp;=\\var{c}\\qquad\\textrm{move }\\var{c}\\\\ \\var{a}x &amp;= \\var{simplify(expression(c+\"-\"+b+\"y\"),[\"basic\",\"unitFactor\"])}\\qquad\\textrm{move }\\var{b}y\\textrm{ to the right}\\\\ x&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+a+\"-\"+b+\"/\"+a+\"y\"),[\"basic\",\"unitFactor\",\"unitDenominator\"])}\\qquad\\textrm{Divide by }\\var{a}\\\\x&amp;=\\var[fractionNumbers]{simplify(expression(c+\"/\"+a+\"-\"+b+\"/\"+a+\"y\"),[\"all\"])}\\end{align}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "formula": {"name": "formula", "group": "Ungrouped variables", "definition": "[substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"a*x+b*y=c\")),\n  substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"a*x+b*y-c=0\"))]", "description": "", 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"group": "Ungrouped variables", "definition": "if(sel_variable=0,substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"1/a*(c-b*y)\")),substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"1/b*(c-a*x)\")))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "formula", "sel_formula", "selected_formula", "variables", "sel_variable", "selected_variable", "answer"], "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>\\(\\var{selected_variable}=\\)[[0]]</p>", "gaps": [{"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, "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don 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