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{"name": "Terry's copy of Straight lines: graphing y=mx+b by finding some points", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "", "showQuestionGroupNames": false, "variable_groups": [], "functions": {"twopoints": {"definition": "\nvar div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',{boundingBox:[-13,13,13,-13],grid:true,axis:false});\nvar board = div.board;\n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = board.create('ticks',[xaxis,2],{\n  drawLabels: true,\n  label: {offset: [-4, -10]},\n  minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,2],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\nvar x1 = 0;\nvar y1 = 0;\nvar x2 = 2;\nvar y2 = 0;\n\n\n\nvar a = board.create('point',[x1,y1],{name:'$y$ int',snapSizeX:1,snapSizeY:1,snapToGrid:true,showInfobox:false});\na.on('drag',function(){\n  var x1 = Numbas.math.niceNumber(a.X());\n  var y1 = Numbas.math.niceNumber(a.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(x1);//could just have x instead of a.X()\n  Numbas.exam.currentQuestion.parts[0].gaps[1].display.studentAnswer(y1);\n});\n\nvar b = board.create('point',[x2,y2],{name:'next nice point',snapSizeX:1,snapSizeY:1,snapToGrid:true,showInfobox:false});\nb.on('drag',function(){\n  var x2 = Numbas.math.niceNumber(b.X());\n  var y2 = Numbas.math.niceNumber(b.Y());\n  Numbas.exam.currentQuestion.parts[0].gaps[2].display.studentAnswer(x2);//could just have x instead of a.X()\n  Numbas.exam.currentQuestion.parts[0].gaps[3].display.studentAnswer(y2);\n});\n\n\nvar line = board.create('line',[a,b], {strokeColor:'#00ff00',strokeWidth:2});\n\n\nquestion.signals.on('HTMLAttached',function(e) {\n  ko.computed(function(){ \n  var x1 = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n  var y1 = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n  if(!(isNaN(x1) || isNaN(y1)) && board.mode!=board.BOARD_MODE_DRAG) {\n  a.moveTo([x1,y1],100);//what does the 100 do?\n  }\n  var x2 = parseFloat(question.parts[0].gaps[2].display.studentAnswer());\n  var y2 = parseFloat(question.parts[0].gaps[3].display.studentAnswer());\n  if(!(isNaN(x2) || isNaN(y2)) && board.mode!=board.BOARD_MODE_DRAG) {\n  b.moveTo([x2,y2],100);//what does the 100 do?\n  }    \n  });\n});\n\nreturn div;\n\n", "language": "javascript", "type": "html", "parameters": []}, "tableofvalues": {"definition": "\nvar div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',{boundingBox:[-13,13,13,-13],grid:true,axis:false});\nvar board = div.board;\n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = board.create('ticks',[xaxis,2],{\n  drawLabels: true,\n  label: {offset: [-4, -10]},\n  minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,2],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\nvar y0 = 0;\nvar y1 = 0;\nvar y2 = 0;\n\nvar glide0 = board.create('line',[[0,0],[0,1]],{visible: false});\nvar glide1 = board.create('line',[[1,0],[1,1]],{visible: false});\nvar glide2 = board.create('line',[[2,0],[2,1]],{visible: false});\n\nvar a = board.create('glider',[0,0,glide0],{name:'',showInfobox:false,snapSizeX:.01,snapSizeY:.01,snapToGrid:true});\na.on('drag',function(){\n  var y0 = Numbas.math.niceNumber(a.Y());\n  Numbas.exam.currentQuestion.parts[1].gaps[0].display.studentAnswer(y0);\n});\n\nvar b = board.create('glider',[0,1,glide1],{name:'',showInfobox:false,snapSizeX:.01,snapSizeY:.01,snapToGrid:true});\nb.on('drag',function(){\n  var y1 = Numbas.math.niceNumber(b.Y());\n  Numbas.exam.currentQuestion.parts[1].gaps[1].display.studentAnswer(y1);\n});\n\nvar c = board.create('glider',[0,2,glide2],{name:'',showInfobox:false,snapSizeX:.01,snapSizeY:.01,snapToGrid:true});\nc.on('drag',function(){\n  var y2 = Numbas.math.niceNumber(c.Y());\n  Numbas.exam.currentQuestion.parts[1].gaps[2].display.studentAnswer(y2);\n});\n\n\nvar lineab = board.create('line',[a,b],{strokeWidth:2,strokeColor:'#00ff00',straightLast:false});\nvar linebc = board.create('line',[b,c],{strokeWidth:2,strokeColor:'#00ff00',straightFirst:false});\n\n  function evaluate(expression) {\n    try {\n      var val = Numbas.jme.evaluate(expression,question.scope);\n      return Numbas.jme.unwrapValue(val);\n    }\n    catch(e) {\n      // if there's an error, return no number\n      return NaN;\n    }\n  }\n\n\nquestion.signals.on('HTMLAttached',function(e) {\n  ko.computed(function(){ \n  var y0 = evaluate(question.parts[1].gaps[0].display.studentAnswer());\n  if(!(isNaN(y0)) && board.mode!=board.BOARD_MODE_DRAG) {\n  a.moveTo([0,y0],100);//what does the 100 do?\n  }\n  var y1 = evaluate(question.parts[1].gaps[1].display.studentAnswer());\n  if(!(isNaN(y1)) && board.mode!=board.BOARD_MODE_DRAG) {\n  b.moveTo([0,y1],100);//what does the 100 do?\n  }\n  var y2 = evaluate(question.parts[1].gaps[2].display.studentAnswer());\n  if(!(isNaN(y2)) && board.mode!=board.BOARD_MODE_DRAG) {\n  c.moveTo([0,y2],100);//what does the 100 do?\n  }    \n  });\n});\n\nreturn div;\n\n", "language": "javascript", "type": "html", "parameters": []}}, "rulesets": {}, "parts": [{"stepsPenalty": 0, "steps": [{"marks": 0, "prompt": "<p>Following the written instructions above. You can drag the points on the graph to help determine the coordinates.</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "information", "showCorrectAnswer": true}], "prompt": "<p>In sketching or graphing a straight line, we only need to plot two points and then draw the straight line through them. Any two points will do, but&nbsp;it is&nbsp;easier to plot when the&nbsp;coordinates are&nbsp;whole numbers.</p>\n<p>One method is to find the $y$-intercept and then use the gradient to find another \"nice\" point.&nbsp;</p>\n<p></p>\n<p>Given the equation $y=\\simplify{{rise}/{run} x +{b}}$ the $y$-intercept gives us the coordinates $\\bigg($[[0]],&nbsp;[[1]]$\\bigg)$, then by going up {rise} and across {run} (that is, using the gradient) we get to the coordinates $\\bigg($[[2]],&nbsp;[[3]]$\\bigg)$.</p>\n<p></p>\n<p>{twopoints()}</p>\n<p></p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "marks": 1, "scripts": {}, "minValue": "0", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "0", "allowFractions": false, "showPrecisionHint": false, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "marks": 1, "scripts": {}, "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{b}", "allowFractions": false, "showPrecisionHint": false, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "marks": 1, "scripts": {}, "minValue": "{run}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{run}", "allowFractions": false, "showPrecisionHint": false, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "marks": 1, "scripts": {}, "minValue": "{rise+b}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{rise+b}", "allowFractions": false, "showPrecisionHint": false, "showCorrectAnswer": true}], "type": "gapfill", "showCorrectAnswer": true}, {"stepsPenalty": 0, "steps": [{"marks": 0, "prompt": "<p>Take the values of $x$ provided in the table and substitute them into the equation for $y$. Put each $y$ value in the table under the corresponding $x$ value. Once you are finished the points on the graph should&nbsp;form a straight line.&nbsp;&nbsp;If they don't it is likely some of your values are incorrect.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, say you have $y=\\frac{2}{3}x-1$, and we need to fill in the following table of values</p>\n<table rules=\"all\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">2</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$y$</td>\n<td style=\"text-align: center;\">&nbsp; &nbsp; &nbsp; &nbsp;</td>\n<td style=\"text-align: center;\">&nbsp; &nbsp; &nbsp; &nbsp;</td>\n<td style=\"text-align: center;\">&nbsp; &nbsp; &nbsp; &nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>We take $x=0$ and substitute it into&nbsp;$y=\\frac{2}{3}x-1$&nbsp;and get&nbsp;$y=\\frac{2}{3}\\times 0 -1=-1$.</p>\n<p>We take $x=1$ and substitute it into&nbsp;$y=\\frac{2}{3}x-1$&nbsp;and get&nbsp;$y=\\frac{2}{3}\\times 1&nbsp;-1=-\\frac{1}{3}$.</p>\n<p>We take $x=2$ and substitute it into&nbsp;$y=\\frac{2}{3}x-1$&nbsp;and get&nbsp;$y=\\frac{2}{3}\\times 2&nbsp;-1=\\frac{1}{3}$.<br/><br/>So we fill the table out as shown:</p>\n<p></p>\n<table rules=\"all\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">2</td>\n</tr>\n<tr>\n<td>$y$</td>\n<td>&nbsp; &nbsp;-1 &nbsp; &nbsp;</td>\n<td>&nbsp; &nbsp; -1/3 &nbsp; &nbsp;</td>\n<td>&nbsp; &nbsp; 1/3 &nbsp; &nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "information", "showCorrectAnswer": true}], "prompt": "<p>Another common method (to find points on a&nbsp;line) is to use a table of values.</p>\n<p></p>\n<p>Given the equation $y=\\simplify{{rise1}/{run1} x+ {b1}}$ fill in the table of values:</p>\n<table rules=\"all\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">2</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$y$</td>\n<td style=\"text-align: center;\">[[0]]</td>\n<td style=\"text-align: center;\">[[1]]</td>\n<td style=\"text-align: center;\">[[2]]</td>\n</tr>\n</tbody>\n</table>\n<p>Notice, with this approach we are more likely to get fractions (which are often a bit harder to plot).</p>\n<p>{tableofvalues()}</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"correctAnswerFraction": true, "marks": 1, "scripts": {}, "minValue": "{b1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{b1}", "allowFractions": true, "showPrecisionHint": false, "showCorrectAnswer": true}, {"correctAnswerFraction": true, "marks": 1, "scripts": {}, "minValue": "{rise1}/{run1}+{b1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{rise1}/{run1}+{b1}", "allowFractions": true, "showPrecisionHint": false, "showCorrectAnswer": true}, {"correctAnswerFraction": true, "marks": 1, "scripts": {}, "minValue": "{2*rise1}/{run1}+{b1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "maxValue": "{2*rise1}/{run1}+{b1}", "allowFractions": true, "showPrecisionHint": false, "showCorrectAnswer": true}], "type": "gapfill", "showCorrectAnswer": true}], "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"js": "", "css": ""}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": "\n"}, "ungrouped_variables": ["b", "run", "rise", "b1", "run1", "rise1"], "variables": {"run": {"definition": "random(2,3,5,7)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "run"}, "run1": {"definition": "random(2,3,5,7)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "run1"}, "b": {"definition": "random(-12..5 except 0)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b"}, "b1": {"definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b1"}, "rise": {"definition": "if(run=2,random(1,3,5,7),if(run=3,random(1,2,4,5,7),if(run=5,random(1,2,3,4,6,7),if(run=7,random(1,2,3,4,5,6)))))", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "rise"}, "rise1": {"definition": "if(run1=2,random(1,3,5,7,9,11),if(run1=3,random(1,2,4,5,7,8,10),if(run1=5,random(1,2,3,4,6,7,8,9),if(run1=7,random(1,2,3,4,5,6,8,9,10,11)))))", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "rise1"}}, "tags": ["gradient intercept", "graphing straight lines", "linear", "plotting points", "straight lines", "table of values"], "name": "Terry's copy of Straight lines: graphing y=mx+b by finding some points", "type": "question", "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}