Using the two point format for equation of a line involving points (x₁, y₁) and (x₂, y₂)
Equation:
(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)
For (-12, -8) and (-17, -16) x₁ = -12, y₁ = -8, x₂ = -17, y₂ = -16
(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)
(y - -8)/(-16 - -8) = (x - -12)/(-17 - -12)
(y + 8)/(-16 + 8) = (x +12)/(-17 +12)
(y + 8)/(8 - 16) = (x +12)/(12 -17)
(y + 8)/(-8) = (x +12)/(-5) Cancel the minus signs on both sides
(y + 8)/(8) = (x +12)/(5)
5*(y + 8) = 8*(x + 12)
5y + 5*8 = 8*x + 8*12
5y + 40 = 8x + 96
5y = 8x + 96 - 40
5y = 8x + 36
Hence the equation of the line is 5y = 8x + 36
