// Numbas version: exam_results_page_options
{"name": "Simon's copy of Straight-line graph values", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"x4": {"group": "Ungrouped variables", "definition": "random(-5..5 except [x1,x2,x3])", "templateType": "anything", "description": "", "name": "x4"}, "c": {"group": "Ungrouped variables", "definition": "random(-10..10)", "templateType": "anything", "description": "", "name": "c"}, "x2": {"group": "Ungrouped variables", "definition": "random(-5..5 except x1)", "templateType": "anything", "description": "", "name": "x2"}, "y1": {"group": "Ungrouped variables", "definition": "(m*x1)+c", "templateType": "anything", "description": "", "name": "y1"}, "y3": {"group": "Ungrouped variables", "definition": "(m*x3)+c", "templateType": "anything", "description": "", "name": "y3"}, "x1": {"group": "Ungrouped variables", "definition": "random(-5..5)", "templateType": "anything", "description": "", "name": "x1"}, "y4": {"group": "Ungrouped variables", "definition": "(m*x4)+c", "templateType": "anything", "description": "", "name": "y4"}, "x3": {"group": "Ungrouped variables", "definition": "random(-5..5 except [x1,x2])", "templateType": "anything", "description": "", "name": "x3"}, "m": {"group": "Ungrouped variables", "definition": "random(-10..10)", "templateType": "anything", "description": "", "name": "m"}, "y2": {"group": "Ungrouped variables", "definition": "(m*x2)+c", "templateType": "anything", "description": "", "name": "y2"}}, "advice": "<p><strong>(a)</strong></p>\n<p>Substitute<strong>&nbsp;</strong>$x=\\var{x1}$ into the equation $y = \\simplify{{m}x + {c}}$</p>\n<p>Hence&nbsp;$y = \\var{m} \\times&nbsp; \\var{x1} + \\var{c}=\\var{m*x1+c}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>Substitute<strong>&nbsp;</strong>$x=\\var{x2}$ into the equation $y = \\simplify{{m}x + {c}}$</p>\n<p>Hence&nbsp;$y = \\var{m} \\times&nbsp;&nbsp;\\var{x2} + \\var{c}=\\var{m*x2+c}$</p>\n<p><strong></strong></p>\n<p><strong>(c)</strong></p>\n<p>First make $x$ the subject of $y = \\simplify{{m}x + {c}}$</p>\n<p>Hence&nbsp;$x = \\frac{y-\\var{c}}{\\var{m}}$</p>\n<p></p>\n<p>Substituting<strong>&nbsp;</strong>your value of $y=\\var{y3}$ into the&nbsp;above equation gives:</p>\n<p>$x= &nbsp;\\frac{\\var{y3}-\\var{c}}{\\var{m}}=\\var{(y3-c)/m}$</p>\n<p><strong></strong></p>\n<p><strong>(d)</strong></p>\n<p>First make $x$ the subject of $y = \\simplify{{m}x + {c}}$</p>\n<p>Hence&nbsp;$x = \\frac{y-\\var{c}}{\\var{m}}$</p>\n<p></p>\n<p>Substituting<strong>&nbsp;</strong>your value of $y=\\var{y4}$ into the&nbsp;above equation gives:</p>\n<p>$x=&nbsp;&nbsp;\\frac{\\var{y4}-\\var{c}}{\\var{m}}=\\var{(y4-c)/m}$</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Finding x and y values for straight line graphs</p>"}, "ungrouped_variables": ["m", "c", "x1", "y1", "x2", "y2", "x3", "y3", "x4", "y4"], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"maxValue": "y1", "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "showFeedbackIcon": true, "minValue": "y1", "customName": "", "type": "numberentry", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showFractionHint": true, "variableReplacements": [], "marks": 1, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>What is $y$ if $x = \\var{x1}$?</p>", "customMarkingAlgorithm": "", "useCustomName": false, "correctAnswerStyle": "plain"}, {"maxValue": "y2", "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "showFeedbackIcon": true, "minValue": "y2", "customName": "", "type": "numberentry", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showFractionHint": true, "variableReplacements": [], "marks": 1, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>What is $y$ if $x = \\var{x2}$?</p>", "customMarkingAlgorithm": "", "useCustomName": false, "correctAnswerStyle": "plain"}, {"maxValue": "x3", "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "showFeedbackIcon": true, "minValue": "x3", "customName": "", "type": "numberentry", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showFractionHint": true, "variableReplacements": [], "marks": 1, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>What is $x$ if $y = \\var{y3}$?</p>", "customMarkingAlgorithm": "", "useCustomName": false, "correctAnswerStyle": "plain"}, {"maxValue": "x4", "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "showFeedbackIcon": true, "minValue": "x4", "customName": "", "type": "numberentry", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showFractionHint": true, "variableReplacements": [], "marks": 1, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>What is $x$ if $y = \\var{y4}$?</p>", "customMarkingAlgorithm": "", "useCustomName": false, "correctAnswerStyle": "plain"}], "statement": "<p>For the line $y = \\simplify{{m}x + {c}}$:</p>", "name": "Simon's copy of Straight-line graph values", "tags": [], "functions": {}, "rulesets": {}, "extensions": [], "variable_groups": [], "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}