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interpreting_linear_equations.html
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interpreting_linear_equations.html
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<!DOCTYPE html>
<html data-require="math math-format graphie word-problems">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Interpreting linear equations</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars"></div>
<div class="problems">
<div id="increase" data-weight="3">
<div class="vars">
<var id="INDEX">randRange( 0, 2 )</var>
<var id="M">1 / randRange( 2, 5 )</var>
<var id="B">randRange( 1, 3 )</var>
<var id="UNIT">[ deskItem( 0 ), fruit( 0 ), "X" ][ INDEX ]</var>
<var id="X_AXIS_LABEL">[ "# of " + plural( UNIT ), "# of " + plural( UNIT ), "X" ][ INDEX ]</var>
<var id="Y_AXIS_LABEL">[ "Price of " + plural( UNIT ), "Price of " + plural( UNIT ), "Y" ][ INDEX ]</var>
<var id="X_AXIS_QUESTION">[ "the number of " + plural( UNIT ), "the number of " + plural( UNIT ), "X" ][ INDEX ]</var>
<var id="Y_AXIS_QUESTION">[ "the price of " + plural( UNIT ), "the price of " + plural( UNIT ), "Y" ][ INDEX ]</var>
</div>
<div class="question">
<p><b>How does <var>Y_AXIS_QUESTION</var> change as <var>X_AXIS_QUESTION</var> increases?</b></p>
<div class="graphie" id="grid">
init({
range: [[-3, 10], [-1, 10]],
scale: [30, 30]
});
grid( [10, 10], [10, 10], {
stroke: "#ccc"
});
style({
stroke: "#888",
strokeWidth: 2,
arrows: "->"
});
path( [ [-0.5, 0], [10, 0] ] );
path( [ [0, -0.5], [0, 10] ] );
style({
stroke: "#000000",
strokeWidth: 0.9,
arrows: "->"
});
label( [ 0, 9.2 ], "\\text{" + Y_AXIS_LABEL + "}", "right");
label( [ 8.5, 0], "\\text{" + X_AXIS_LABEL + "}", "below");
style({
stroke: "#6495ED",
strokeWidth: 2,
arrows: "->"
});
plot( function( x ) {
return ( M ) * x + B;
}, [0, 10]);
</div>
</div>
<div class="solution">Increases</div>
<ul class="choices" data-category="true">
<li>Increases</li>
<li>Decreases</li>
<li>Stays the same</li>
</ul>
<div class="hints">
<div>
<div class="graphie" data-update="grid">
style({ fill: "", stroke: "#000000" });
line( [ 4, 4 * M + B ], [ 7, 4 * M + B ] );
style({ stroke: "#40a020" });
line( [ 7, 4 * M + B ], [ 7, 7 * M + B ] );
</div>
<p>Looking at the graph, we see that as <code>x</code> increases (<code>\color{#000000}{\text{black arrow}}</code>), <code>y</code> also increases (<code>\color{#40a020}{\text{green arrow}}</code>).</p>
</div>
<p>We can say that the slope of the line is positive, or that the variables have a direct relationship.</p>
<p>Thus, as <var>X_AXIS_QUESTION</var> increases, <var>Y_AXIS_QUESTION</var> also <b>increases</b>.</p>
</div>
</div>
<div id="decrease" data-type="increase" data-weight="3">
<div class="vars">
<var id="M">1 / randRange( 2, 5 ) * -1</var>
<var id="B">randRange( 6, 8 )</var>
</div>
<div class="solution">Decreases</div>
<div class="hints">
<div>
<div class="graphie" data-update="grid">
style({ fill: "", stroke: "#000000" });
line( [ 4, 4 * M + B ], [ 7, 4 * M + B ] );
style({ stroke: "#ff0000" });
line( [ 7, 4 * M + B ], [ 7, 7 * M + B ] );
</div>
<p>Looking at the graph, we see that as <code>x</code> increases (<code>\color{#000000}{\text{black arrow}}</code>), <code>y</code> decreases (<code>\color{#ff0000}{\text{red arrow}}</code>).</p>
</div>
<p>We can say that the slope of the line is negative, or that the variables have an inverse relationship.</p>
<p>Thus, as <var>X_AXIS_QUESTION</var> increases, <var>Y_AXIS_QUESTION</var> <b>decreases</b>.</p>
</div>
</div>
<div id="stays" data-type="increase" data-weight="1">
<div class="vars">
<var id="M">0</var>
<var id="B">randRange( 2, 8 )</var>
</div>
<div class="solution">Stays the same</div>
<div class="hints">
<p>Looking at the graph, we see that as <code>x</code> increases, there is no change in <code>y</code>.</p>
<p>We can say that the slope of the line is zero, or that the variables have no correlation.</p>
<p>Thus, as <var>X_AXIS_QUESTION</var> increases, <var>Y_AXIS_QUESTION</var> <b>stays the same</b>.</p>
</div>
</div>
<div data-weight="7" id="identifypoint">
<!-- Ensure the X and Y deltas of the beginning and end of the line are at least
five. -->
<div class="vars" data-ensure="abs( LINESTART[ 0 ] - LINEEND[ 0 ] ) >= 5 && abs( LINESTART[ 1 ] - LINEEND[ 1 ] ) >= 5">
<!-- When X is the solution ensure that Y isn't 0 and vice versa so that the line
added by the first hint doesn't cover up an axis. -->
<div data-ensure="POINTX === SOLUTION ? POINTY !== 0 : POINTX !== 0">
<var id="POINTX, POINTY">randRange( -9, 9, 2 )</var>
<var id="SOLUTION">randFromArray([ POINTX, POINTY ])</var>
</div>
<var id="LINESTART">
(function() {
var lineStartX,
lineStartY;
if (randFromArray([ false, true ])) {
lineStartX = randFromArray([ -10, 10 ]);
lineStartY = randRange( -10, 10 );
} else {
lineStartX = randRange( -10, 10 );
lineStartY = randFromArray([ -10, 10 ]);
}
return [ lineStartX, lineStartY ];
})()
</var>
<var id="LINEEND">
(function() {
var lineEndX = POINTX,
lineEndY = POINTY,
newXDelta,
newYDelta,
xDelta = -( LINESTART[ 0 ] - POINTX ),
yDelta = -( LINESTART[ 1 ] - POINTY );
// Reduce xDelta and yDelta until their absolute values are less than or equal
// to one.
if ( Math.abs( xDelta ) > Math.abs( yDelta ) ) {
newXDelta = xDelta > 0 ? 1 : -1;
newYDelta = yDelta * newXDelta / xDelta;
} else {
newYDelta = yDelta > 0 ? 1 : -1;
newXDelta = xDelta * newYDelta / yDelta;
}
xDelta = newXDelta;
yDelta = newYDelta;
while ( Math.abs( lineEndX ) < 10 && Math.abs( lineEndY ) < 10 ) {
lineEndX += xDelta;
lineEndY += yDelta;
}
return [ lineEndX, lineEndY ];
})()
</var>
</div>
<div class="question">
<p data-if="POINTX === SOLUTION">What is <code>x</code> when <code>y</code> is <code><var>POINTY</var></code>?</p>
<p data-else>What is <code>y</code> when <code>x</code> is <code><var>POINTX</var></code>?</p>
<div class="graphie" id="graph">
graphInit({
range: 10,
scale: 20,
axisArrows: "<->",
tickStep: 2,
labelStep: 1,
});
label( [ 0, 10], "y", "below right");
label( [ 10, 0], "x", "above left");
style({ stroke: '#6495ed' });
line( LINESTART, LINEEND );
</div>
</div>
<div class="hints">
<div>
<div class="graphie" data-update="graph">
var lineStart, lineEnd;
if ( POINTX === SOLUTION ) {
lineStart = [ -10, POINTY ];
lineEnd = [ 10, POINTY ];
} else {
lineStart = [ POINTX, -10 ];
lineEnd = [ POINTX, 10 ];
}
line( lineStart, lineEnd, {
stroke: '#28ae7b',
strokeDasharray: '- '
});
</div>
<p data-if="POINTX === SOLUTION">The dashed <span style="color: #28ae7b;">green</span> line shows where <code>y</code> is <code><var>POINTY</var></code>.</p>
<p data-else>The dashed <span style="color: #28ae7b;">green</span> line shows where <code>x</code> is <code><var>POINTX</var></code>.</p>
</div>
<p>The <span style="color: #6495ed;">blue</span> and dashed <span style="color: #28ae7b;">green</span> lines meet at <code>(<var>POINTX</var>, <var>POINTY</var>)</code>.</p>
<p>Therefore <code><var>POINTX === SOLUTION ? 'x' : 'y'</var></code> is <code><var>SOLUTION</var></code>.</p>
</div>
<div class="solution" data-forms="integer" data-type="multiple">
<p><code><var>POINTX === SOLUTION ? 'x' : 'y'</var> =</code> <span class="sol" data-forms="integer"><var>SOLUTION</var></span></p>
</div>
</div>
</div>
</div>
</body>
</html>