#### Answer

$3x+2y=-9$

#### Work Step by Step

Rewrite in slope-intercept form.
$-2x+3y=9$
$-2x+3y+2x=2x+9$
$3y=2x+9$
$y=\frac{2}{3}x+3$
The slope of this line is $\frac{2}{3}x+3$ which means that the slope of the line perpendicular to this will be $-\frac{3}{2}$
Therefore, the tentative equation of the line is
$y=-\frac{3}{2}x+b$
Substitute $x=-1$ and $y=3$ to find the value of $b$ since we know that this line passes through the point $(-1,-3)$.
$-3=-\frac{3}{2} \cdot(-1) + b\\$
$-3=\frac{3}{2}+b\\$
$-3-\frac{3}{2}=b\\$
$-\frac{6}{2}-\frac{3}{2}=b\\$
$-\frac{9}{2}=b$
Thus, the equation of the line is $y= -\frac{3}{2}x - \frac{9}{2}$.
Rewrite in standard form by multiplying $2$ to both sides of the equation.
$2(y) = 2\left(-\frac{3}{2}x-\frac{9}{2}\right)\\
2y=-3x-9\\
3x + 2y = -9$