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