Slope-intercept form can be written as
y = mx + b
From the question above, we should move x to another side (right side), so the left side only contains of y-variable
-3x + 2y = 12
2y = 12 + 3x
To make slope-intercept form, only y is on the left side. We should move the coefficient 2 to the right side.
2y = 12 + 3x
2y = 3x + 12
y = (3x + 12)/2
Simplify the equation
y = (3x + 12)/2
y = (3/2)x + 12/2
y = (3/2)x + 6
This is the final answer ⇒ y = (3/2)x + 6