Verified Answer :

naǫ

Convert the equation to the slope-intercept form.
\(4y-6x+12=0 \\ 4y=6x-12 \ \ \ |\div 4 \\ y=\frac{6}{4}x-\frac{12}{4} \\ y=\frac{3}{2}x-3\)

In the \(y=mx+b\) form, \(m\) is the slope.
\(y=\frac{3}{2}x-3 \\ m=\frac{3}{2}=1\frac{1}{2}\)

The slope is equal to \(1 \frac{1}{2}\).

\(4y-6x+12=0\\ 4y=6x-12\\ y=\dfrac{6}{4}x-\dfrac{12}{4}\\ y=\dfrac{3}{2}x-3\\\\\\ m=\dfrac{3}{2}\)