Answer
The slope of the line is $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$.
Work Step by Step
Consider the following equation of a line:
$Ax+By=C$
The slope-intercept form of a line with slope m and y intercept b is as follows:
$y=mx+b$
Rearrange the equation in standard slope-intercept form of $y=mx+c$ by solving the equation for y. Bring all the variables other than y and constant terms to one side.
$\begin{align}
& Ax+By=C \\
& By=-Ax+C
\end{align}$
Divide both sides by B to get,
$\begin{align}
& \frac{By}{B}=\frac{-Ax+C}{B} \\
& y=-\frac{A}{B}x+\frac{C}{B}
\end{align}$
On comparing this equation $y=-\frac{A}{B}x+\frac{C}{B}$ with the slope–intercept form of a line $y=mx+b$, we can observe that $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$.
Hence, the slope of the line is $m=-\frac{A}{B}$ and the y-intercept is $b=\frac{C}{B}$.
