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<!DOCTYPE html>
<html data-require="math math-format expressions graphie interactive">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>Graphing systems of equations</title>
    <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
    <div class="problems">
        <div id="standard" data-weight="4">
            <div class="vars">
                <div data-ensure="( YINT_1 + SLOPE_1_FRAC[0] &lt;= 10 ) &amp;&amp; ( YINT_2 + SLOPE_2_FRAC[0] &lt;= 10 ) &amp;&amp; ( YINT_1 + SLOPE_1_FRAC[0] &gt;= -10 ) &amp;&amp; ( YINT_2 + SLOPE_2_FRAC[0] &gt;= -10 )">
                    <var id="X">randRangeNonZero( -5, 5 )</var>
                    <var id="Y">randRange( -5, 5 )</var>
                    <div data-ensure="( abs(YINT_1 - YINT_2) &gt; 3 ) &amp;&amp; ( YINT_1 !== Y ) &amp;&amp; ( YINT_2 !== Y )">
                        <var id="YINT_1">randRangeNonZero( -5, 5 )</var>
                        <var id="YINT_2">randRangeNonZero( -5, 5 )</var>
                    </div>
                    <var id="SLOPE_1">(Y - YINT_1) / X</var>
                    <var id="SLOPE_2">(Y - YINT_2) / X</var>
                    <var id="SLOPE_1_FRAC">toFraction( SLOPE_1, 0.001 )</var>
                    <var id="SLOPE_2_FRAC">toFraction( SLOPE_2, 0.001 )</var>
                </div>
                <var id="PRETTY_SLOPE_1">SLOPE_1 === 1 ? "" : ( SLOPE_1 === -1 ? "-" : decimalFraction( SLOPE_1, true, true ) )</var>
                <var id="PRETTY_SLOPE_2">SLOPE_2 === 1 ? "" : ( SLOPE_2 === -1 ? "-" : decimalFraction( SLOPE_2, true, true ) )</var>
                <var id="MULT_1">randRangeNonZero( -2, 2 )</var>
                <var id="MULT_2">randRangeNonZero( -2, 2 )</var>
                <var id="A1">( Y - YINT_1 ) * -MULT_1</var>
                <var id="A2">( Y - YINT_2 ) * -MULT_2</var>
                <var id="B1">X * MULT_1</var>
                <var id="B2">X * MULT_2</var>
                <var id="C1">X * YINT_1 * MULT_1</var>
                <var id="C2">X * YINT_2 * MULT_2</var>
                <var id="STD_FORM_1">true</var>
                <var id="STD_FORM_2">true</var>
            </div>

            <p class="question">Graph this system of equations and solve.</p>

            <div class="problem">
                <p class="hint_blue" data-if="STD_FORM_1">
                    <code><var>expr([ "+", [ "*", A1, "x" ], [ "*", B1, "y" ] ])</var> = <var>C1</var></code>
                </p>
                <p class="hint_blue" data-else="">
                    <code>y = <var>PRETTY_SLOPE_1</var> x + <var>YINT_1</var></code>
                </p>

                <p class="hint_green" data-if="STD_FORM_2">
                    <code><var>expr([ "+", [ "*", A2, "x" ], [ "*", B2, "y" ] ])</var> = <var>C2</var></code>
                </p>
                <p class="hint_green" data-else="">
                    <code>y = <var>PRETTY_SLOPE_2</var> x + <var>YINT_2</var></code>
                </p>

                <div class="graphie" id="grid">
                    graphInit({
                        range: 11,
                        scale: 20,
                        axisArrows: "&lt;-&gt;",
                        tickStep: 1,
                        labelStep: 1
                    });

                    addMouseLayer();
                    graph.pointA = addMovablePoint({
                        coord: [ -5, 5 ],
                        snapX: 0.5,
                        snapY: 0.5,
                        normalStyle: {
                            stroke: KhanUtil.BLUE,
                            fill: KhanUtil.BLUE
                        }
                    });
                    graph.pointB = addMovablePoint({
                        coord: [ 5, 5 ],
                        snapX: 0.5,
                        snapY: 0.5,
                        normalStyle: {
                            stroke: KhanUtil.BLUE,
                            fill: KhanUtil.BLUE
                        }
                    });
                    graph.pointC = addMovablePoint({
                        coord: [ -5, -5 ],
                        snapX: 0.5,
                        snapY: 0.5,
                        normalStyle: {
                            stroke: KhanUtil.GREEN,
                            fill: KhanUtil.GREEN
                        }
                    });
                    graph.pointD = addMovablePoint({
                        coord: [ 5, -5 ],
                        snapX: 0.5,
                        snapY: 0.5,
                        normalStyle: {
                            stroke: KhanUtil.GREEN,
                            fill: KhanUtil.GREEN
                        }
                    });
                    graph.line1 = addMovableLineSegment({
                        pointA: graph.pointA,
                        pointZ: graph.pointB,
                        fixed: true,
                        extendLine: true
                    });
                    graph.line2 = addMovableLineSegment({
                        pointA: graph.pointC,
                        pointZ: graph.pointD,
                        fixed: true,
                        extendLine: true,
                        normalStyle: {
                            "stroke": KhanUtil.GREEN,
                            "stroke-width": 2
                        }
                    });

                    graph.showCorrect1 = function() {
                        graph.pointA.moveTo( 0, YINT_1, true );
                        graph.pointB.moveTo( SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0], true );
                    };

                    graph.showCorrect2 = function() {
                        graph.pointC.moveTo( 0, YINT_2, true );
                        graph.pointD.moveTo( SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0], true );
                    };

                    // A and B can't be in the same place
                    graph.pointA.onMove = function( x, y ) {
                        return ( x != graph.pointB.coord[0] || y != graph.pointB.coord[1] );
                    }
                    graph.pointB.onMove = function( x, y ) {
                        return ( x != graph.pointA.coord[0] || y != graph.pointA.coord[1] );
                    }

                    // C and D can't be in the same place
                    graph.pointC.onMove = function( x, y ) {
                        return ( x != graph.pointD.coord[0] || y != graph.pointD.coord[1] );
                    }
                    graph.pointD.onMove = function( x, y ) {
                        return ( x != graph.pointC.coord[0] || y != graph.pointC.coord[1] );
                    }

                    graph.pointC.toFront();
                    graph.pointD.toFront();
                    graph.pointA.toFront();
                    graph.pointB.toFront();

                </div>
                <p>Click and drag the points to move the lines.</p>
            </div>
            <div class="solution" data-type="multiple">
                <p><code>x = </code> <span class="sol"><var>X</var></span></p>
                <p><code>y = </code> <span class="sol"><var>Y</var></span></p>
                <div class="sol" data-type="custom">
                    <div class="instruction">
                        Your graphs are also part of your answer.
                    </div>
                    <div class="guess">
                        [ graph.pointA.coord, graph.pointB.coord, graph.pointC.coord, graph.pointD.coord ]
                    </div>
                    <div class="validator-function">
                        var slope1 = ( guess[1][1] - guess[0][1] ) / ( guess[1][0] - guess[0][0] );
                        var slope2 = ( guess[3][1] - guess[2][1] ) / ( guess[3][0] - guess[2][0] );
                        var yint1 = slope1 * ( 0 - guess[0][0] ) + guess[0][1];
                        var yint2 = slope2 * ( 0 - guess[2][0] ) + guess[2][1];
                        // allows blue function to be graphed with green line and vice versa, fwiw
                        var graphCorrect = ( abs( SLOPE_1 - slope1 ) &lt; 0.001
                            &amp;&amp; abs( SLOPE_2 - slope2 ) &lt; 0.001
                            &amp;&amp; abs( YINT_1 - yint1 ) &lt; 0.001
                            &amp;&amp; abs( YINT_2 - yint2 ) &lt; 0.001 )
                            || ( abs( SLOPE_1 - slope2 ) &lt; 0.001
                            &amp;&amp; abs( SLOPE_2 - slope1 ) &lt; 0.001
                            &amp;&amp; abs( YINT_2 - yint1 ) &lt; 0.001
                            &amp;&amp; abs( YINT_1 - yint2 ) &lt; 0.001 );
                        var pointCorrect = parseInt($("#solutionarea input").eq(0).val()) === X &amp;&amp;
                            parseInt($("#solutionarea input").eq(1).val()) === Y;

                        if (pointCorrect &amp;&amp; !graphCorrect) {
                            return "You found the right solution to the system of equations, but you haven't graphed them correctly.";
                        }
                        return graphCorrect;
                    </div>
                    <div class="show-guess">
                        graph.pointA.setCoord( guess[0] );
                        graph.pointB.setCoord( guess[1] );
                        graph.pointC.setCoord( guess[2] );
                        graph.pointD.setCoord( guess[3] );
                        graph.line1.transform( true );
                        graph.line2.transform( true );
                    </div>
                </div>
                <div class="example">two integers like <code>6</code></div>
            </div>
        </div>
        <div id="slope-intercept" data-type="standard" data-weight="5">
            <div class="vars">
                <var id="STD_FORM_1">false</var>
                <var id="STD_FORM_2">false</var>
            </div>
        </div>
        <div id="mixed" data-type="standard" data-weight="1">
            <div class="vars">
                <var id="STD_FORM_1">random() &lt; 0.5 ? true : false</var>
                <var id="STD_FORM_2">!STD_FORM_1</var>
            </div>
        </div>
    </div>

    <div class="hints">
        <div data-if="STD_FORM_1" data-unwrap="">
            <p class="hint_blue">
                Convert the first equation,
                <code><var>expr([ "+", [ "*", A1, "x" ], [ "*", B1, "y" ] ])</var> = <var>C1</var></code>,
                to slope-intercept form.
            </p>
            <p class="hint_blue"><code>y = <var>PRETTY_SLOPE_1</var> x + <var>YINT_1</var></code></p>
        </div>
        <p class="hint_blue">
            The y-intercept for the first equation is <code><var>YINT_1</var></code>, so the first line
            must pass through the point <code>(0, <var>YINT_1</var>)</code>.
        </p>
        <p class="hint_blue">
            <span data-if='abs( SLOPE_1_FRAC[0] ) !== 1'>The slope for the first equation is <code><var>decimalFraction( SLOPE_1, true, true )</var></code>. Remember that
            the slope tells you rise over run. So in this case for every
            <code><var>abs( SLOPE_1_FRAC[0] )</var></code>
            positions
            you move
            <span data-if="SLOPE_1_FRAC[0] < 0"><em>down</em> (because it's negative)</span>
            <span data-else="">up</span>.</span><span data-else="">The slope for the first equation is <code><var>decimalFraction( SLOPE_1, true, true )</var></code>. Remember that
            the slope tells you rise over run. So in this case for every
            <code><var>abs( SLOPE_1_FRAC[0] )</var></code>
            position
            you move
            <span data-if="SLOPE_1_FRAC[0] < 0"><em>down</em> (because it's negative)</span>
            <span data-else="">up</span>.</span>
            <span data-if='abs( SLOPE_1_FRAC[1] ) !== 1'>You must also move
            <code><var>SLOPE_1_FRAC[1]</var></code>
            positions
            to the right.</span><span data-else="">You must also move
            <code><var>SLOPE_1_FRAC[1]</var></code>
            position
            to the right.</span>
        </p>
        <p class="hint_blue">
            <span data-if='abs( SLOPE_1_FRAC[1] ) !== 1'><code><var>SLOPE_1_FRAC[1]</var></code>
            positions to the right.</span><span data-else=""><code><var>SLOPE_1_FRAC[1]</var></code>
            position to the right.</span>
            <span data-if='abs( SLOPE_1_FRAC[0] ) !== 1'><code><var>abs( SLOPE_1_FRAC[0] )</var></code>
            positions
            <span data-if="SLOPE_1_FRAC[0] < 0">down</span><span data-else="">up</span> from
            <code>(0, <var>YINT_1</var>)</code> is
            <code>(<var>SLOPE_1_FRAC[1]</var>, <var>YINT_1 + SLOPE_1_FRAC[0]</var>)</code>.</span><span data-else=""><code><var>abs( SLOPE_1_FRAC[0] )</var></code>
            position
            <span data-if="SLOPE_1_FRAC[0] < 0">down</span><span data-else="">up</span> from
            <code>(0, <var>YINT_1</var>)</code> is
            <code>(<var>SLOPE_1_FRAC[1]</var>, <var>YINT_1 + SLOPE_1_FRAC[0]</var>)</code>.</span>
        </p>
        <p class="hint_blue">
            Graph the blue line so it passes through
            <code>(0, <var>YINT_1</var>)</code> and
            <code>(<var>SLOPE_1_FRAC[1]</var>, <var>YINT_1 + SLOPE_1_FRAC[0]</var>)</code>.
            <br><input onclick="javascript:
KhanUtil.currentGraph.graph.showCorrect1();
" type="button" value="Show me">
        </p>
        <div data-if="STD_FORM_2" data-unwrap="">
            <p class="hint_green">
                Convert the second equation,
                <code><var>expr([ "+", [ "*", A2, "x" ], [ "*", B2, "y" ] ])</var> = <var>C2</var></code>,
                to slope-intercept form.
            </p>
            <p class="hint_green"><code>y = <var>PRETTY_SLOPE_2</var> x + <var>YINT_2</var></code></p>
        </div>
        <p class="hint_green">
            The y-intercept for the second equation is <code><var>YINT_2</var></code>, so the second line
            must pass through the point <code>(0, <var>YINT_2</var>)</code>.
        </p>
        <p class="hint_green">
            <span data-if='abs( SLOPE_2_FRAC[0] ) !== 1'>The slope for the second equation is <code><var>decimalFraction( SLOPE_2, true, true )</var></code>. Remember that
            the slope tells you rise over run. So in this case for every
            <code><var>abs( SLOPE_2_FRAC[0] )</var></code>
            positions
            you move
            <span data-if="SLOPE_2_FRAC[0] < 0"><em>down</em> (because it's negative)</span>
            <span data-else="">up</span>.</span><span data-else="">The slope for the second equation is <code><var>decimalFraction( SLOPE_2, true, true )</var></code>. Remember that
            the slope tells you rise over run. So in this case for every
            <code><var>abs( SLOPE_2_FRAC[0] )</var></code>
            position
            you move
            <span data-if="SLOPE_2_FRAC[0] < 0"><em>down</em> (because it's negative)</span>
            <span data-else="">up</span>.</span>
            <span data-if='abs( SLOPE_1_FRAC[1] ) !== 1'>You must also move
            <code><var>SLOPE_2_FRAC[1]</var></code>
            positions
            to the right.</span><span data-else="">You must also move
            <code><var>SLOPE_2_FRAC[1]</var></code>
            position
            to the right.</span>
        </p>
        <p class="hint_green">
            <span data-if='abs( SLOPE_2_FRAC[1] ) !== 1'><code><var>SLOPE_2_FRAC[1]</var></code>
            positions to the right.</span><span data-else=""><code><var>SLOPE_2_FRAC[1]</var></code>
            position to the right.</span>
            <span data-if='abs( SLOPE_2_FRAC[0] ) !== 1'><code><var>abs( SLOPE_2_FRAC[0] )</var></code>
            positions
            <span data-if="SLOPE_2_FRAC[0] < 0">down</span><span data-else="">up</span> from
            <code>(0, <var>YINT_2</var>)</code> is
            <code>(<var>SLOPE_2_FRAC[1]</var>, <var>YINT_2 + SLOPE_2_FRAC[0]</var>)</code>.</span><span data-else=""><code><var>abs( SLOPE_2_FRAC[0] )</var></code>
            position
            <span data-if="SLOPE_2_FRAC[0] < 0">down</span><span data-else="">up</span> from
            <code>(0, <var>YINT_2</var>)</code> is
            <code>(<var>SLOPE_2_FRAC[1]</var>, <var>YINT_2 + SLOPE_2_FRAC[0]</var>)</code>.</span>
        </p>
        <p class="hint_green">
            Graph the green line so it passes through
            <code>(0, <var>YINT_2</var>)</code> and
            <code>(<var>SLOPE_2_FRAC[1]</var>, <var>YINT_2 + SLOPE_2_FRAC[0]</var>)</code>.
            <br><input onclick="javascript:
KhanUtil.currentGraph.graph.showCorrect2();
" type="button" value="Show me">
        </p>
        <p>
            The solution is the point where the two lines intersect.
        </p>
        <div>
            <p>
                The lines intersect at <code class="hint_pink">(<var>X</var>, <var>Y</var>)</code>.
            </p>
            <div class="graphie" data-update="grid">
                style({ stroke: PINK });
                circle( [ X, Y ], 0.5 );
            </div>
        </div>
    </div>

</div>
</body>
</html>
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