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