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

**Solution:**

Given that, (x_{1}, y_{1}) = (-3, 2) and (x_{2}, y_{2}) = (-5, 8)

The two-point form of a line passing through these two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is:

(y − y_{1}) = [(y_{2} − y_{1}) (x − x_{1})] / (x_{2} − x_{1})

⇒ (y − y_{1}) (x_{2} − x_{1}) = (y_{2} − y_{1}) (x − x_{1})

Substitute the values of points (x_{1}, y_{1}) and (x_{2}, y_{2})

(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.

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