// Numbas version: exam_results_page_options {"name": "Ida's copy of Sp\u00f8rsm\u00e5l 1", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ida's copy of Sp\u00f8rsm\u00e5l 1", "tags": [], "metadata": {"description": "

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

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The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

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This particular example has a positive gradient.

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En rett linje går gjennom de to punktene med koordinatene $A=(\\var{xa},\\var{ya})$ og  $B=(\\var{xb},\\var{yb})$.

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{plotPoints()}

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Vi finner ekvasjonen for ei rett linje gjennom å først finne stigningstallet til linja.

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a)

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Vi finner stigningstallet ($a$) ved å bruke punktene $A = (x_1,y_1)=(\\var{xa},\\var{ya})$ og $B = (x_2,y_2)=(\\var{xb},\\var{yb})$.

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Vi får da

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\\begin{align}
a &= \\frac{y_2-y_1}{x_2-x_1} \\\\[0.5em]
&= \\frac{\\simplify[!collectNumbers]{{yb}-{ya}}}{\\simplify[!collectNumbers]{{xb}-{xa}}} \\\\[0.5em]
&= \\frac{\\simplify[]{{yb}-{ya}}}{\\simplify{{xb}-{xa}}} \\\\[0.5em]
&= \\simplify[simplifyFractions,unitDenominator]{({yb-ya})/({xb-xa})}\\text{.}
\\end{align}

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b)

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Sett nå in stigningstallet og et av punktene i ettpunktsformelen.

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size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', fixed: true, showInfobox: true});\nvar b = board.create('point',[xb,yb],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',fixed: true, showInfobox: true});\n\n\n//ans(was tree) is defined at the end and nscope looks important\n//but they're both variables\n var ans;\n var nscope = new Numbas.jme.Scope([scope,{variables:{x:new Numbas.jme.types.TNum(0)}}]);\n//this is the beating heart of whatever plots the function,\n//I've changed this from being curve to functiongraph\n var line = board.create('functiongraph',[function(x){\nif(ans) {\n try {\nnscope.variables.x.value = x;\n var val = Numbas.jme.evaluate(ans,nscope).value;\n return val;\n }\n catch(e) {\nreturn 13;\n }\n}\nelse\n return 13;\n },-12,12]\n , {strokeColor:\"blue\",strokeWidth: 4} );\n \nvar correct_line = 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Stigningstallet $a$ til en linje gjennom to punkter $(x_{1},y_{1})$ og $(x_{2},y_{2})$ er gitt ved

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$a=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Finn stigningstallet til linja ved bruk av punktene som er gitt i koordinatsystemet over.

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$a=$ [[0]]

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En rett linje som går gjennom punktet $(x_{1},y_{1})$ og har stigningstallet $a$, er gitt ved likninga

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$y-y_{1}=a(x-x_{1})$.

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Finn likninga til den rette linja som går gjennom punktene A og B i koordinatsystemet over. Skriv svaret på formen $y=ax+b$

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$\\displaystyle y=$ [[0]]

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You must input your answer in the form y = mx +c where m and c are numbers.

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