Blog Post

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

Grade 9

Grade 10

Grade 11

Grade 12


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



<ul class="wp-block-list">
<li>Write an equation of a line parallel to given line</li>



<li>Understand the slope of perpendicular lines</li>



<li>Write an equation of a line perpendicular to a given line</li>
</ul>



<h2 class="wp-block-heading">Parallel and Perpendicular Lines&nbsp;&nbsp;</h2>



<h3 class="wp-block-heading">Parallel Lines</h3>



<p>Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.&nbsp;&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-3825.png" alt="Parallel lines: " class="wp-image-20479" style="width:395px;height:157px" width="395" height="157" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3825.png 553w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3825-300x119.png 300w" sizes="auto, (max-width: 395px) 100vw, 395px" /></figure></div>


<h3 class="wp-block-heading">Perpendicular Lines&nbsp;</h3>



<p>Perpendicular lines are lines that intersect at a right (90 degrees) angle.&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-3826.png" alt="Perpendicular lines: " class="wp-image-20480" style="width:352px;height:352px" width="352" height="352" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3826.png 660w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3826-300x300.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3826-150x150.png 150w" sizes="auto, (max-width: 352px) 100vw, 352px" /></figure></div>


<h3 class="wp-block-heading">Write an equation of a line Parallel to given line&nbsp;</h3>



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



<p>What is the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to the graph of y=4x -7?&nbsp;</p>



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



<p>Identify the slope of the given line.&nbsp;</p>



<p>y = 4x – 7&nbsp;</p>



<p>The slope is 4. The slope of a parallel line will be the same.&nbsp;</p>



<p><strong>Step 2:</strong>&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>Start with point form. Use the given point and the slope of the parallel line.&nbsp;</p>



<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3827.png" alt="step 2" class="wp-image-20488" style="width:548px;height:58px" width="548" height="58" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3827.png 548w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3827-300x32.png 300w" sizes="auto, (max-width: 548px) 100vw, 548px" /></figure>



<p>y- 5 = 4 (x+3)&nbsp;</p>



<p>y-5 = 4x +12&nbsp;</p>



<p>y= 4x +17&nbsp;</p>



<p>The equation of the line is y= 4x +17.&nbsp;</p>



<h3 class="wp-block-heading">Understand the slope of perpendicular lines&nbsp;</h3>



<p><strong>Why does it make sense that the slopes of perpendicular lines have opposite signs?</strong>&nbsp;</p>



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



<p>Perpendicular lines are a bit more complicated.&nbsp;</p>



<p>If you visualize a line with a positive slope (so it&#8217;s an increasing line), then the perpendicular line must have a negative slope (because it will have to be a decreasing line).&nbsp;&nbsp;</p>



<p>So, perpendicular lines have slopes which have opposite signs.&nbsp;</p>



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



<p>Find the slope of a line perpendicular to the line y = −4x + 9.&nbsp;</p>



<p>They&#8217;ve given me the original line&#8217;s equation, and it&#8217;s in &#8220;<em>y </em>=&#8221; form, so it&#8217;s easy to find the slope.&nbsp;&nbsp;</p>



<p>I can just read the value of the equation: <em>m</em> = −4.&nbsp;</p>



<p>This slope can be turned into a fraction by putting it over 1, so this slope can be restated as:&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-3829.png" alt="example" class="wp-image-20491" style="width:112px;height:52px" width="112" height="52"/></figure></div>


<p>To get the negative reciprocal, I need to flip this fraction and change the sign.&nbsp;&nbsp;</p>



<p>Then the slope of any line perpendicular to the given line is:&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="118" height="58" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3828.png" alt="example" class="wp-image-20490"/></figure></div>


<h3 class="wp-block-heading">Write an equation of a line perpendicular to a given line&nbsp;</h3>



<p><strong>Example:</strong>&nbsp;<strong>What is the equation to the line that passes through (6, -5) and is perpendicular to the graph of y=2x+3?</strong>&nbsp;</p>



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



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



<p>Use the slope of the given line to determine the slope of the line that is perpendicular.&nbsp;</p>



<p>y=2x+3.&nbsp;</p>



<p>m = 2&nbsp;</p>



<p>The slope of a line perpendicular to the given line is the opposite reciprocal of&nbsp; 2 / 1</p>



<p>Use −1 / 2 as the slope of new line.&nbsp;</p>



<p><strong>Step 2: </strong>Start with the point-slope form. Use the given point and slope of the perpendicular line.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="225" height="68" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3830.png" alt="step 2" class="wp-image-20492"/></figure></div>


<p>y+5 = −1 / 2&nbsp; (x &#8211; 6)&nbsp;</p>



<p>The graph of y + 5 = −1 / 2  (x &#8211; 6) passes through the point (6, -5) and is perpendicular to the graph of y=2x+3.&nbsp;</p>



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



<ol class="wp-block-list" type="1">
<li>What is the equation of the line parallel to y=3x+5 and through the point (1, 7)?</li>



<li>What is the equation of the line parallel to y=4x+3 and through the point (5, 9)?</li>



<li>What is the equation of the line that is perpendicular to y=2x+10 and goes through the point (5, 1)?</li>



<li>What is the equation of the line parallel to y= 3/4x+1 and through the point (-4, 9)?</li>



<li>Determine the equation of a line perpendicular to y=3x−2 at the point (2, 4).</li>



<li>What is the equation of the line that passes through (4, 5) and is perpendicular to the graph of y=2x-3?</li>



<li>Define parallel lines.</li>



<li>Define perpendicular lines.</li>



<li>Are the graph of the equations 4y=2x-5 and y=-2x +7 parallel, perpendicular, or neither?</li>



<li>Write the equation of a line that is perpendicular to y=−1/2 x+4 and goes through the point (0, 6)?</li>
</ol>



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


<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-3831-1024x547.png" alt="Concept Map " class="wp-image-20494" style="width:758px;height:404px" width="758" height="404" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3831-1024x547.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3831-300x160.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3831-768x410.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3831.png 1483w" sizes="auto, (max-width: 758px) 100vw, 758px" /></figure></div>


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



<ul class="wp-block-list">
<li>Understand <a href="https://www.turito.com/learn/math/parallel-and-perpendicular-lines">parallel and perpendicular lines</a></li>



<li>Write an equation of a line Parallel to given line</li>



<li>Understand the slope of perpendicular lines</li>



<li>Understand how to write an equation of a line perpendicular to a given line.</li>
</ul>
