Answer
$y=-\frac{2}{3}x$
Work Step by Step
Step 1. The slope of the line $3x-2y=6$ is $m_1=\frac{3}{2}$ and the line perpendicular to it will have a slope of $m=-\frac{1}{m_1}=-\frac{2}{3}$
Step 2. Point $(-6,4)$ is on the line, we can write the equation as $y-4=-\frac{2}{3}(x+6)$ or $y=-\frac{2}{3}x$ in the slope-intercept form.
