The inverse is found by writing x in terms of y: x=(3-y)/2 or 3/2-y/2.
An arbitrary set of 4 points could be for y=-1, 0, 1, 3 giving x=2, 3/2, 1, 0.
The points are (x,y)=(2,-1), (3/2,0), (1,1), (0,3) which, of course, also satisfy the original equation.