y = mx + n
m slope = Δy / Δx
for point(-7,43) and (4,-12)
Δy = -12 - 43 = -55
Δx = 4 - (-7) = 11
m = - 55/11 = -5
choose a point for instance point (-7,43) and insert it into the equation, you get:
43 = -5 * (-7) + n = + 35 + n
n = 43 - 35 = 8
so:
y = -5x + 8