Answer
The equation of the perpendicular line is
$ y=-\frac{1}{4}x+\frac{9}{4}$.
Work Step by Step
The given point is $(-3,3)$.
The given equation of the line is
$\Rightarrow 2y=8x-6$
Slope-intercept form is
$\Rightarrow y=4x-3$
Slope of the line is $m=4$.
Slope of the perpendicular line is $m=-\frac{1}{4}$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $-\frac{1}{4}$ for $m,-3$ for $x,$ and $3$ for $y$.
$\Rightarrow 3=-\frac{1}{4}(-3)+b$
Simplify.
$\Rightarrow 3=\frac{3}{4}+b$
Subtract $\frac{3}{4}$ from each side.
$\Rightarrow 3-\frac{3}{4}=\frac{3}{4}+b-\frac{3}{4}$
Simplify.
$\Rightarrow \frac{12-3}{4}=b$
$\Rightarrow \frac{9}{4}=b$
The equation of the perpendicular line is
$\Rightarrow y=-\frac{1}{4}x+\frac{9}{4}$.
