Question

Write the equation in slope-intercept form through the point (4, -4) and is perpendicular to the line y = -4x - 2 and graph.

Answer 1

$y=\frac{1}{4}x-5$

Explanation

Step 1

when 2 lines are perpendicular, the product of their slopes is equal to -1

$\begin{gathered} if \\ \text{y}_1\perp y_2 \\ \text{then} \\ slope_1\cdot slope_2=-1 \end{gathered}$

Now, we have

$\begin{gathered} y=-4x-2\Rightarrow y=mx+b \\ \text{Hence} \\ m_1=\text{slope1}=-4 \end{gathered}$

use the equation to find slope2 ( the slope of the line we are looking for)

$\begin{gathered} slope_1\cdot slope_2=-1 \\ -4\cdot m_2=-1 \\ m_2=\frac{-1}{-4}=\frac{1}{4} \\ \\ \text{slope}2=\frac{1}{4} \end{gathered}$

Step 2

find the eq using:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{Let} \\ m=\text{slope}2=\frac{1}{4} \\ P(x_1,y_1)=(4,-4) \end{gathered}$

replacing

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{4}(x-4) \\ y+4=\frac{1}{4}x-\frac{4}{4} \\ y=\frac{1}{4}x-1-4 \\ y=\frac{1}{4}x-5 \end{gathered}$

I hope this helps you