Answer
The value of slope is wrong.
The correct equation of the line is
$y=-3x+7$
Work Step by Step
The given point is $(x_1,y_1)=(4,-5)$.
The given equation of the line is
$\Rightarrow y=\frac{1}{3}x+5$
Slope of the line is $m=\frac{1}{3}$.
Slope of the perpendicular line is $m=-3$.
The point-slope form is
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $-3$ for $m,4$ for $x_1,$ and $-5$ for $y_1$.
$\Rightarrow y-(-5)=-3(x-4)$
Use distributive property.
$\Rightarrow y+5=-3x+12$
Subtract $5$ from each side.
$\Rightarrow y+5-5=-3x+12-5$
Simplify.
$\Rightarrow y=-3x+7$
Hence, the value of slope is wrong.
The correct equation of the line is
$y=-3x+7$
