Answer
$m=-\frac{A}{B}$,
Work Step by Step
The general slope-intercept form of a line is:
$y=mx+b$, where $m$ is the slope, and $(x,y)$ can be the coordinates of any point on the line.
Hence I express $y$: $Ax+By=C\\By=C-Ax\\y=\frac{C}{B}-\frac{A}{B}x$
Thus the slope of the line is $m=-\frac{A}{B}$, which is the slope of all parallel lines to this line.
