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<h2 class="wp-block-heading">Key Concepts</h2>



<ul class="wp-block-list"><li>Understand point slope form of a linear equation</li><li>Write an equation in point slope form</li><li>Sketch the graph of a linear equation in point slope form</li><li>Apply linear equations</li></ul>



<h3 class="wp-block-heading">Point–Slope form </h3>



<p>The point-slope form of a linear equation is&nbsp;</p>



<p>y – y<sub>1</sub> = m(x – x<sub>1</sub>) &nbsp;</p>



<p>Where <em>m</em> is the slope and (<em>x</em><sub>1, </sub>y<sub>1</sub>) is the specific point and (x, y) is any point on the line.&nbsp;</p>



<h3 class="wp-block-heading">Understand point-slope form of a linear equation </h3>



<p><strong>1. How can you write the equation of a line using any points on a line? </strong></p>



<ul class="wp-block-list"><li>Use the slope formula to find the slope using the specific point (x<sub>1, </sub>y<sub>1) </sub>and any point (x, y) </li></ul>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3767-1024x354.png" alt="Point Slope Form" class="wp-image-20367" width="716" height="247" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3767-1024x354.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3767-300x104.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3767-768x265.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3767.png 1367w" sizes="auto, (max-width: 716px) 100vw, 716px" /></figure></div>

<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="296" height="192" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3768.png" alt="Point Slope Form" class="wp-image-20369"/></figure></div>


<p>We can write the equation of a line using any point (x<sub>1, </sub>y<sub>1</sub>) and the slope <em>m</em> in point-slope form.&nbsp;&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<p>y &#8211; y<sub>1</sub> = m (x &#8211; x<sub>1</sub>)&nbsp;</p>



<ul class="wp-block-list" start="2"><li>How to find the equation of a line with slope and coordinates of a point? <ol><li>Identify the point coordinates. </li><li>Identify the slope.  </li><li>Input the values into the point-slope form formula: y &#8211; y<sub>1</sub> = m (x &#8211; x<sub>1</sub>).  </li><li>Simplify to get the general equation.  </li></ol></li></ul>



<h3 class="wp-block-heading">Write an equation in point-slope form </h3>



<p>1. <strong>Write the equation for the line that passes through point (3, 1) with a slope of 3.</strong> </p>



<p><strong>Solution:</strong> </p>



<p>The slope and a point on the line are known, so use point-slope form.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="579" height="127" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3769.png" alt="Write an equation in point-slope form " class="wp-image-20371" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3769.png 579w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3769-300x66.png 300w" sizes="auto, (max-width: 579px) 100vw, 579px" /></figure></div>


<p>The equation in point–slope form is y+1 = 3x -9.&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<p>2. <strong>Write an equation for a line that passes through the following points (-4, 4) and (6, 9)</strong> </p>



<p><strong>Solution:</strong> </p>



<p>Find the slope of the line using the two given points.&nbsp;</p>



<p>=y<sub>2</sub>−y<sub>1</sub> / x<sub>2</sub>−x<sub>1</sub></p>



<p>= 9−4 / 6−(−4)&nbsp;&nbsp;</p>



<p>= 5 / 10</p>



<p>=1 / 2</p>



<p>Use slope and one point to write the equation.&nbsp;</p>



<p>y – y<sub>1</sub> = m(x – x<sub>1</sub>)&nbsp;</p>



<p>y-4<strong> =</strong> 1 / 2 (x+4)&nbsp;</p>



<p>y-4 = 1 / 2x +2 </p>



<p>The equation in point –slope form is y-4 =  1 / 2x +2 </p>



<h3 class="wp-block-heading">Sketch the graph of a linear equation in point-slope form </h3>



<p><strong>Example 1:</strong>&nbsp;</p>



<p><strong>What is the graph of y−2=</strong> 𝟐 / 𝟑 <strong>(x+2)?</strong></p>



<p><strong>Solution:</strong> </p>



<p><strong>Step 1:</strong>&nbsp;</p>



<p>Identify a point on the line from the equation and plot it.&nbsp;</p>



<p>y−2= 2 / 3 (x+2)  </p>



<p>The point is (-2, 2)&nbsp;</p>



<p><strong>Step 2:</strong>&nbsp;</p>



<p>Use the slope to plot a second point.&nbsp;&nbsp;</p>



<p>m = 2 / 3</p>



<p>Move 2 units up and 3 units to the right and draw another point (1, 4).&nbsp;</p>



<p><strong>Step 3:</strong> Sketch a line through the points.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3778.png" alt="graph" class="wp-image-20383" width="379" height="419" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3778.png 475w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3778-271x300.png 271w" sizes="auto, (max-width: 379px) 100vw, 379px" /></figure></div>


<h3 class="wp-block-heading">Apply linear equations </h3>



<p><strong>Example:</strong>&nbsp;</p>



<p>Paul wants to place an ad in the newspaper. The newspaper charges $10 for the first 2 lines of text and $3 for each additional line of text.&nbsp;</p>



<ol class="wp-block-list"><li>Write an equation in point-slope form that describes the equation. </li><li>Find the cost of an ad that has 8 lines. </li></ol>



<p><strong>Solution:</strong> </p>



<p><strong>1. Write an equation in point slope form that describes the equation. </strong></p>



<p>Points on the line (x<sub>1</sub>, y<sub>1</sub>)<sub> </sub>is (2, 10)&nbsp;</p>



<p>Slope m =3&nbsp;</p>



<p>Equation is&nbsp; y – y<sub>1</sub> = m(x – x<sub>1</sub>)&nbsp;</p>



<p>y-10 = 3 (x-2) </p>



<p><strong>2. Find the cost of an ad that has 8 lines. </strong></p>



<p>y-10 =3 (x-2)&nbsp;</p>



<p>y-10 = 3(8-2)&nbsp;</p>



<p>y – 10 = 24-6 </p>



<p>y –10 = 18 </p>



<p>y = 28&nbsp;</p>



<p>The cost of an ad that has 8 lines is $28. </p>



<h2 class="wp-block-heading">Exercise</h2>



<ol class="wp-block-list" type="1"><li>Write the equation in point-slope form of the line that passes through the given point with the given slope.</li></ol>



<p class="has-text-align-center">(3, 1); m= 2</p>



<ol class="wp-block-list" start="2"><li>Write the equation of the line in point-slope form.</li></ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3782.png" alt="Exercise" class="wp-image-20396" width="259" height="244" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3782.png 351w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3782-300x282.png 300w" sizes="auto, (max-width: 259px) 100vw, 259px" /></figure></div>


<ol class="wp-block-list" type="1" start="3"><li>Write an equation of the line in point–slope form that passes through the given points.</li></ol>



<p>(-4, 12) and (-7, -3)</p>



<ol class="wp-block-list" start="4"><li>Sketch the graph of the given equation.</li></ol>



<p>y-1 = &nbsp;5/4(x+2)</p>



<ol class="wp-block-list" start="5"><li>Write an equation of the line in point–slope form that passes through the given points in each table. Then write the equation in slope-intercept form.</li></ol>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="169" height="300" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3784.png" alt="table" class="wp-image-20398"/></figure></div>


<ol class="wp-block-list" start="6"><li>Write the slope-intercept form of the equation of the line through the given points using point-slope form through: (3, −3) and (0, −5).</li><li>Find the slope of the line that contains the points from the table</li></ol>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="150" height="225" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3787.png" alt="table 2" class="wp-image-20401"/></figure></div>


<ol class="wp-block-list" start="8"><li>Use the graph of the line shown.<ol><li>Write a point-slope form of the equation for the line shown.</li><li>Estimate the value of the y-intercept of the line.</li></ol></li></ol>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="609" height="300" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3789.png" alt="Estimate the value of the y-intercept of the line." class="wp-image-20403" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3789.png 609w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3789-300x148.png 300w" sizes="auto, (max-width: 609px) 100vw, 609px" /></figure></div>


<ol class="wp-block-list" start="9"><li>A railway system on a hillside moves passengers at a constant rate to an elevation of 50 m. The elevation of a train is given for 2 different locations. Write an equation in point-slope form to represent the elevation of the train in terms of the train.</li></ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3790.png" alt="point slope" class="wp-image-20404" width="331" height="254" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3790.png 412w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3790-300x230.png 300w" sizes="auto, (max-width: 331px) 100vw, 331px" /></figure></div>


<ol class="wp-block-list" start="10"><li>Write the slope-intercept form of the equation of the line through the given points using point-slope form through: (3, 1) and (-5, −2).</li></ol>



<h3 class="wp-block-heading">Concept Map</h3>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3791.png" alt="Concept Map:" class="wp-image-20405" width="676" height="250" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3791.png 1012w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3791-300x111.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3791-768x285.png 768w" sizes="auto, (max-width: 676px) 100vw, 676px" /></figure></div>


<h3 class="wp-block-heading">What have we learned</h3>



<ul class="wp-block-list"><li>Understand point slope form of a linear equation</li><li>Write an equation in point slope form</li><li>&nbsp;Find the slope of the line using the&nbsp; two given points.</li><li>Sketch the graph of a linear equation in point slope form</li><li>Apply linear equations</li></ul>
