A Line Passes through (−1, 5) and (1, 3). Which Answer is the Equation of the Line?

We will be using the concept of the Point-Slope Form of a line to solve this. 

Answer: The Equation of the Line Passing through the given Points (-1, 5), (1, 3) is x + y = 4.

Let's solve this step by step.

Explanation:

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

Let's calculate the slope below,

According to the Slope Formula,

(m) = (y₂ − y₁) / (x₂ − x₁)

Substituting the values,

Slope(m) = (3 - 5) / (1 - (-1))

m = -2/2

m = -1

The point-slope formula states (y − y₁) = m (x − x₁).

Substituting the values of (x₁, y₁) = (-1, 5) and m = -1, we get,

(y - 5) = -1 × (x - (-1))

⇒ y - 5 = - x - 1

⇒ x + y = 4

Hence, the equation of the line passing through the given points (-1, 5), (1, 3) is x + y = 4.