Answer
$$ y=-\frac{3}{2}x-6$$
Work Step by Step
Since the slope is $-\frac{3}{2}$, the line equation is
$$ y=-\frac{3}{2}x+c.$$
To find $ c $, we use the fact that the line passes through the point $(4,-12)$
$$-12=-\frac{3}{2}(4)+c\Longrightarrow c=-12+6=-6$$
Hence, the equation is
$$ y=-\frac{3}{2}x-6$$
