Answer
$\frac{B}{A}$.
Work Step by Step
The given equation of the line is
$\Rightarrow Ax+By=C$
Isolate $y$.
Subtract $Ax$ from both sides.
$\Rightarrow Ax+By-Ax=C-Ax$
Simplify.
$\Rightarrow By=C-Ax$
Divide both sides by $B$.
$\Rightarrow \frac{By}{B}=\frac{C-Ax}{B}$
Simplify.
$\Rightarrow y=\frac{C}{B}-\frac{Ax}{B}$
$\Rightarrow y=-\frac{A}{B}x+\frac{C}{B}$
This is in the slope-intercept form.
$\Rightarrow y=mx+c$
Where slope of the line is $m=-\frac{A}{B}$.
Two lines are perpendicular if their slopes are negative reciprocal to each other.
Hence, the slope of the perpendicular line is
$=−\frac{1}{m}$
$=−\frac{1}{-\frac{A}{B}}$
Simplify.
$=\frac{B}{A}$.
