How do you find an equation for f(x)

Question

If f(x) is a linear function, f(−2)=4, and f(5)=−4, find an equation for f(x).

Answer 1

(-2,4), (5,-4) are two points on the line with slope = (-4,-4)/(5+2) = -8/7

y-4 = (-8/7)(x+2)

7y-28 = -8x -16

8x+7y = 12