To convert from standard form to slope-intercept form, you need to isolate y, as follows:
3x - 2y = 8
3x - 2y -3x = 8 - 3x subtract 3x at both sides
-2y = 8 - 3x
-2y/(-2) = (8 - 3x)/(-2) divide by -2 at both sides
y = 8/(-2) + (-3x)/(-2) distributing
y = -4 + 3/2x