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<!DOCTYPE html>
<html data-require="math math-format expressions">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
<title>Converting between point slope and slope intercept form</title>
<script src="../khan-exercise.js"></script>
<style type="text/css">
#answer_area input[type=text] {
width: 30px;
<div class="exercise">
<div class="problems">
<div id="point-to-intercept">
<div class="vars" data-ensure="y1 != 0">
<var id="m">(random() > 0.5 ? -1 : 1) * (rand(5) + 1)</var>
<var id="b">(random() > 0.5 ? -1 : 1) * (rand(5) + 1)</var>
<var id="x1">(random() > 0.5 ? -1 : 1) * (rand(3) + 1)</var>
<var id="y1">m*x1+b</var>
<var id="var1">m*x1</var>
<p class="question">Convert the following equation from point slope to slope intercept form.</p>
<p>In other words, if the equation is rewritten to look like <code>y = mx + b</code>, what are the values of <code>m</code> and <code>b</code>?</p>
<p><code>y - <var>y1</var> = <var>m</var>(x - <var>x1</var>)</code></p>
<div class="solution" data-type="multiple">
<p><code>y = \space</code><span class="sol"><var>m</var></span><code>\space \cdot x + \space</code><span class="sol"><var>b</var></span></p>
<div class="hints">
<p>Distribute the <code><var>m</var></code> in the <code class="hint_blue"><var>m</var>(x - <var>x1</var>)</code> term on the right.</p>
<p><code>y - <var>y1</var> = \color{<var>BLUE</var>}{<var>expr([ "*", m, "x" ])</var> - <var>var1</var>}</code></p>
Isolate the y term on the left by
<span data-if="y1 < 0">subtracting <code><var>-y1</var></code> from both sides.</span>
<span data-else>adding <code><var>y1</var></code> to both sides.</span>
<p><code>y = <var>expr([ "*", m, "x" ])</var> - <var>var1</var> + <var>y1</var></code></p>
<p>Combine the constant terms on the right.</p>
<p><code>y = <var>expr([ "*", m, "x" ])</var> + <var>b</var></code></p>
<p>The equation is now in slope-intercept form, with a slope of <code><var>m</var></code> and a y-intercept of <code><var>b</var></code>.</p>
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