2y + 3x = 2
Let's convert to slope-intercept form (y=mx+b) to find the slope.
Move x to the right side.
2y = -3x + 2
Divide by the y coefficient. (2)
y = -3/2x + 1
In slope-intercept form, (y=mx+b) the slope is represented as m.
In this case the slope is -3/2.
Parallel lines have the same slope. Since m(AB) = -3/2, m(CD) = -3/2, too.