Answer
The slope of line perpendicular to $Ax+By+C=0,A\ne 0\text{ and }B\ne 0$ is $\frac{B}{A}$.
Work Step by Step
Consider the function provided $Ax+By+C=0$.
Write the slope intercept form of the equation; isolate y on one side:
$By=-Ax-C$
Divide both sides by $B$ ;
$\begin{align}
& \frac{By}{B}=\frac{-Ax-C}{B} \\
& y=-\frac{A}{B}x-\frac{C}{B}
\end{align}$
The slope of the line is the coefficient of x in the equation $y=ax+b$.
The slope line obtained is:
$-\frac{A}{B}$
The slope of the perpendicular line is the negative reciprocal of $-\frac{A}{B}$.
So, the slope of the perpendicular line is $\frac{B}{A}$.
Thus, the slope of the line perpendicular to $Ax+By+C=0,A\ne 0\text{ and }B\ne 0$ is $\frac{B}{A}$.
