Perpendicular Lines

<p><span style="color:#27ae60;">Perpendicular Lines</span> are two lines that intersect at a 90&deg; angle. What&#39;s that you say? We haven&#39;t studied angles yet. Good point!</p> <p style="margin-left: 40px;"><strong>Coordinate Geometry Definition</strong>: Two lines whose slopes are <u>negative reciprocals</u> of each other.</p> <p><strong><span style="color:#8e44ad;">What&#39;s a &quot;negative reciprocal&quot;?</span></strong></p> <p>Good question. To find the reciprocal of a number, you simply &quot;flip&quot; it. For example, the reciprocal of $3$ is $\frac{1}{3}$. The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.&nbsp;</p> <p>With the negative reciprocal, you not only have to &quot;flip&quot; it but change the sign as well. For example, the negative reciprocal of $-5$ is $\frac{1}{5}$</p> <p><strong><span style="color:#8e44ad;">Example</span></strong></p> <p>What is the slope of a line that is perpendicular to the line with the equation $4x-5y = 20$.</p> <p style="margin-left: 40px;"><strong>Step 1</strong>: Convert into the $y=mx+b$ format to easily find the slop.</p> <p>$$4x-5y=20$$</p> <p>$$-5y=-4x+20$$</p> <p>$$y = \frac{4}{5}x-4$$</p> <p style="margin-left: 40px;"><strong>Step 2</strong>: Take the slope from step 1 ($\frac{4}{5}$) and flip it.</p> <p>$$\frac{4}{5} \rightarrow \frac{5}{4}$$</p> <p style="margin-left: 40px;"><strong>Step 3</strong>: Make it the opposite sign.</p> <p>$$\frac{5}{4} \rightarrow -\frac{5}{4}$$</p> <p>&nbsp;</p>