Answer
Point slope $y-3=\frac{3}{2}(x+1)$
Slope intercept form $y=\frac{2}{2}x+\frac{9}{2}$
Work Step by Step
To be parallel the equation must have the same slope of the given equation
$3x-2y=5$ we transform it in a slope intercept form
$-2y=5-3x$
$y=\frac{3}{2}x-\frac{5}{2}$
$m=\frac{3}{2}$
For the point slope we use the following $y-y_{1}=m(x-x_{1})$ and plug in the known values $m=\frac{3}{2} $ and $(-1,3)$
Point slope $y-3=\frac{3}{2}(x+1)$
For the slope intercept for we solve for y and simplify
$y-3=\frac{3}{2}(x+1)$
$y=\frac{3}{2}x+\frac{3}{2}+3$
$y=\frac{2}{2}x+\frac{9}{2}$
