Answer
$y=\frac{2}{3}x-\frac{5}{3}$
Work Step by Step
$3x+2y=5$
$2y=5-3x$
$y=\frac{5}{2}-\frac{3}{2}x$
The slope of the new line is the negative reciprocal of $\frac{-3}{2}$: $-\frac{2}{3}$.
Use point slope form:
$y+3=\frac{2}{3}(x+2)$
$y=\frac{2}{3}x+\frac{4}{3}-3$
$y=\frac{2}{3}x-\frac{5}{3}$
