What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?

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