Question

through: (-4,-4), perpendicular to y=4x-2

Answer 1

First let's determine the slope of the straight line

A perpendicular line fulfills the following relationship

$m1m2=-1$

Where

m1 = slope of the first straight line

m2 = slope of the perpendicular straight line

$\begin{gathered} 4m2=-1 \\ m2=-\frac{1}{4} \end{gathered}$

Now we are going to calculate the intersection point

$\begin{gathered} b=y-mx \\ b=-4-(-\frac{1}{4})\cdot(-4) \\ b=-4-1 \\ b=-5 \end{gathered}$

The equation of the line that passes through the point (-4,-4) with a slope of -1/4

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