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Slope = (-12 - 43)/(4 +7) = -55/11 = -5

y = mx + b
43 = -5(-7) + b
43=35+b
b = 8

equation
y = -5x + 8

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

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