The original line's equation is y = -2x + 3
To find inverse of a function, you switch y and x and then solve for y =.
x = -2y + 3
x-3 = -2y
(x-3)/-2 = y

You can then guess and check.
If x is 0:
(0-3)/-2 = 3/2 ≠3
If x is 3:
(3-3)/-2 = 0 = 0
Check the others just to make sure.
If x is 1:
(1-3)/-2 = 1 ≠ -1
If x is -1:
(-1-3)/-2 = 2 ≠ 5