What is the Equation of the Line that Passes through the Points (−3, 2) and (−5, 8)?

Solution:

Given that, (x₁, y₁) = (-3, 2) and (x₂, y₂) = (-5, 8)

The two-point form of a line passing through these two points (x₁, y₁) and (x₂, y₂) is:

(y − y₁) = [(y₂ − y₁) (x − x₁)] / (x₂ − x₁)

⇒ (y − y₁) (x₂ − x₁) = (y₂ − y₁) (x − x₁)

Substitute the values of points (x₁, y₁) and (x₂, y₂)

(y − 2) ({-5} − {-3}) = (8 − 2) (x − {-3})

(y − 2) (-2) = (6) (x + 3)

-2y + 4 = 6x + 18

6x + 2y + 14 = 0

3x + y + 7 = 0

Hence, the equation of the line that passes through the points (−3, 2) and (−5, 8) is 3x + y + 7 = 0

What is the equation of the line that passes through the points (-3, 2) and (-5, 8)?

Summary:

The equation of the line that passes through the points (-3, 2) and (-5, 8) is  3x + y + 7 = 0.