# Find the Equation for a Line that Passes through the Two Points (−1,3) and (4,−5).

**Solution:**

We will be using the two-point form of a line to solve this.

Let's solve this step by step.

Given that, (x_{1}, y_{1}) = (-1, 3) and (x_{2}, y_{2}) = (4, -5)

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 − 3) (4 − {-1}) = ({-5} − 3) (x − {-1})

(y − 3) (5) = (-8) (x + 1)

5y - 15 = -8x - 8

8x + 5y - 7 = 0

Hence, the equation of the line that passes through the two points(−1,3) and (4,−5) is 8x + 5y - 7 = 0

## Find the Equation for a Line that Passes through the Two Points (−1,3) and (4,−5).

**Summary:**

The Equation of the Line that Passes through the Two Points (−1,3) and (4,−5) is 8x + 5y - 7 = 0.

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