// Numbas version: exam_results_page_options {"name": "Edward's copy of Use student input in a JSXGraph diagram", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

{eqnline(a,b,x2,y2)}

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The above graph shows a line which has an equation of the form $y=ax+b$, where $a$ and $b$ are integers.

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You are given two points on the line, $(0,\\var{b})$ and $(\\var{x2},\\var{y2})$, as indicated on the diagram.

", "extensions": ["jsxgraph"], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"showFeedbackIcon": true, "prompt": "

Write the equation of the line in the diagram. The line described by your equation will also be drawn on the diagram.

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$y=\\;$[]

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There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "name": "Edward's copy of Use student input in a JSXGraph diagram", "ungrouped_variables": ["x2", "b", "a", "y2"], "tags": [], "rulesets": {}, "advice": "\n

First Method.

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You are given that the line goes through $(0,\\var{b})$ and $(-1,\\var{b-a})$ and the equation of the line is of the form $y=ax+b$

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Hence:

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1) At $x=0$ we have $y=\\var{b}$, and this gives $\\var{b}=a \\times 0 +b =b$ on putting $x=0$ into $y=ax+b$.

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So $b=\\var{b}$.

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2) At $x=-1$ we have $y=\\var{b-a}$, and this gives $\\var{b-a}=a \\times (-1) +b =\\simplify[all,!collectNumbers]{-a+{b}}$ on putting $x=-1$ into $y=ax+b$.

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On rearranging we obtain $a=\\simplify[all,!collectNumbers]{{b}-{b-a}}=\\var{a}$.

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So $a=\\var{a}$.

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So the equation of the line is $\\simplify{y={a}*x+{b}}$.

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Second Method.

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The equation $y=ax+b$ tells us that the graph crosses the $y$-axis (when $x=0$) at $y=b$.

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So looking at the graph we immediately see that $b=\\var{b}$.

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$a$ is the gradient of the line and is given by the change from $(-1,\\var{b-a})$ to $(0,\\var{b})$:

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\$a=\\frac{\\text{Change in y}}{\\text{Change in x}}=\\frac{\\simplify[all,!collectNumbers]{({b-a}-{b})}}{-1-0}=\\var{a}\$

\n\n", "functions": {"eqnline": {"language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["x2", "number"], ["y2", "number"]], "type": "html", "definition": "// This function creates the board and sets it up, then returns an\n// HTML div tag containing the board.\n \n// The line is described by the equation \n// y = a*x + b\n\n// This function takes as its parameters the coefficients a and b,\n// and the coordinates (x2,y2) of a point on the line.\n\n// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in \n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{boundingBox: [-13,16,13,-16],\n axis: false,\n showNavigation: false,\n grid: true\n});\n \n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\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// create the static line based on the coefficients a and b\n//var line1 = board.create('line',[[0,b],[1,a+b]],{fixed:true, strokeWidth: 1});\n\n// mark the two given points - one on the y-axis, and one at (x2,y2)\n//var p1 = board.create('point',[0,b],{fixed:true, size:3, name: 'P_1', face: 'cross'});\n//var p2 = board.create('point',[x2,y2],{fixed:true, size:3, name: 'P_2', face: 'cross'});\n\nreturn div;"}}, "type": "question", "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}]}]}], "contributors": [{"name": "Edward Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1824/"}]}