Answer
Perpendicular line $y=\frac{1}{3}x+6$.
Work Step by Step
The given point is $(-3,5)$.
The given equation of the line is
$\Rightarrow y=-3x-1$
Slope of the line is $m=-3$.
Slope of the perpendicular line is $m=\frac{1}{3}$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $\frac{1}{3}$ for $m,-3$ for $x,$ and $5$ for $y$.
$\Rightarrow 5=\frac{1}{3}(-3)+b$
Simplify.
$\Rightarrow 5=-1+b$
Add $1$ to each side.
$\Rightarrow 5+1=-1+b+1$
Simplify.
$\Rightarrow 6=b$.
The equation of the perpendicular line is
$\Rightarrow y=\frac{1}{3}x+6$.
