// Numbas version: exam_results_page_options {"name": "Linear Functions 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Linear Functions 1", "tags": [], "metadata": {"description": "Rearrange to give for y = mx + c, find gradient and realise that a parallel line has the same gradient (find x_intercept)", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

The equation of a line $L$ is {a}$x + y = ${y_int}

", "advice": "

In part (a) rearrange the equation in the form $y = mx + c$

$y = -${a}$x +$ {y_int}

Gradient = {grad}

In part (b) the y intercept is at (0,{y_int})

In part (c) the equation of the new line is $y = $ {grad}$x + $ {y_int2}, substituting y to be zero will give the x-intercept at ({M_x},{M_y})

", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "

a in equation ax + y = c

", "templateType": "randrange"}, "y_int": {"name": "y_int", "group": "Ungrouped variables", "definition": "random(-3 .. 4#1)", "description": "

y intercept of straight line

", "templateType": "randrange"}, "grad": {"name": "grad", "group": "Ungrouped variables", "definition": "-{a}", "description": "

gradient of line

", "templateType": "anything"}, "y_int2": {"name": "y_int2", "group": "Ungrouped variables", "definition": "random(2 .. 9#1)", "description": "

y intercept of second parallel line

", "templateType": "randrange"}, "M_x": {"name": "M_x", "group": "Ungrouped variables", "definition": "{y_int2}/(-{grad})", "description": "

x-intercept of second parallel line

", "templateType": "anything"}, "M_y": {"name": "M_y", "group": "Ungrouped variables", "definition": "0", "description": "

y coordinate at x-intercept of second line

", "templateType": "number"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "y_int", "grad", "y_int2", "M_x", "M_y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "

Write down the gradient of line $L$.

", "minValue": "{grad}", "maxValue": "{grad}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"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": "

Complete below to give the y-intercept of line $L$

(0,[[0]])

A second line M is parallel to L and passes through point P(0,{y_int2})

The line M intercepts the x-axis at ([[0]],[[1]])

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "M_x", "maxValue": "M_x", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "M_y", "maxValue": "M_y", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}]}], "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}