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

Solution:

The equation of the line passing through two points can be found by using two point form of straight lines.

(x - x₁) / (x₂ - x₁) = (y - y₁) / (y₂ - y₁)

Given, two points are (-12, -8) and (-17, -16).

The equation becomes,

(x - (-12)) / (-17 - (-12)) = (y - (-8)) / (-16 - (-8))

By further calculation,

(x + 12) / (-17 + 12) = (y  +8)/(-16 + 8)

(x + 12)/(-5) = (y + 8)/(-8)

So we get,

(-8)(x + 12) = (-5)(y + 8)

By cross multiplication,

8(x + 12) = 5(y + 8)

Using the multiplicative distributive property,

8x + 96 = 5y + 40

8x - 5y + 56 = 0

Therefore, the equation of the line is 8x - 5y + 56 = 0.

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

Summary:

The equation of the line that passes through the points (-12, -8) and (-17, -16) is 8x - 5y + 56 = 0.