Find the slope of the line through (x1,y1) = (-7,-3) and (x2,y2) = (-12,5)
m = (y2 - y1)/(x2 - x1)
m = (5 - (-3))/(-12 - (-7))
m = (5 + 3)/(-12 + 7)
m = (8)/(-5)
m = -8/5
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Plug m = -8/5 and (x1,y1) = (-7,-3) into the point slope formula. Solve for y.
y - y1 = m(x - x1)
y - (-3) = (-8/5)(x - (-7))
y + 3 = (-8/5)(x + 7)
y + 3 = (-8/5)x + (-8/5)(7) .... distribute
y + 3 = (-8/5)*x - 56/5 .... multiply
y + 3 - 3 = (-8/5)*x - 56/5 - 3 ... subtract 3 from both sides
y = (-8/5)*x - 56/5 - 15/5 ... rewrite "3" as "15/5"
y = (-8/5)*x - 71/5 .... combine like terms
This equation is in slope-intercept form y = mx+b with m = -8/5 = -1.6 as the slope and b = -71/5 = -14.2 as the y intercept.
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If you want the equation in standard form (Ax+By = C), then you could follow these steps shown below
y = (-8/5)*x - 71/5
5y = 5((-8/5)*x - 71/5) ... multiply both sides by 5
5y = -8x - 71
5y+8x = -8x - 71+8x ... add 8x to both sides
8x+5y = -71
This is in the form Ax+By = C with A = 8, B = 5, C = -71.
