Answer
$ 3x + 2y =0 $
Work Step by Step
First, we solve for the slope of the perpendicular line:
$-2x + 3y = 8 \\ 3y = 2x+8 \\ y = 2/3 x +8/3$
Since this is in slope intercept form, we see that the slope is 2/3. Thus, the slope of the perpendicular line is the opposite reciprocal, which is -3/2. Thus, we use point slope form, and then we simplify to standard form:
$y - y_{1} = m(x-x_{1}) \\ y = -3/2(x) \\ 2y = -3x \\ 3x+2y=0$
