Rearrange 3x - 2y = 5 into y = mx + c form:
2y + 5 = 3x
2y = 3x - 5
y = 1.5x - 2.5
The lines must have the same gradient to be parallel and it goes through (-2,2) so you use y - y1 = m(x - x1):
y - 2 = 1.5(x - (-2))
y - 2 = 1.5x + 3
Answer: y = 1.5x + 5