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, (x₁, y₁) = (-1, 3) and (x₂, y₂) = (4, -5)

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 − 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.