Find an Equation of the Line Passing through the given Points. (1, 1), (8, −3).

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, 1), (8, −3) is 4x + 7y = 11.

Let's solve this step by step.

Explanation:

Given: (x₁, y₁) = (1, 1) and (x₂, y₂) = (8, -3)

We need to find the slope first.

By Slope Formula

m = (y₂ − y₁) / (x₂ − x₁)

Substituting the values,

Slope(m) = (-3 - 1) / (8 - 1)

Slope(m) = -4/7

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

Substituting the values we get,

⇒ (y - 1) = (- 4/7) × (x - 1) 

⇒ 7(y - 1) = -4(x - 1) 

⇒ 7y - 7 = - 4x + 4

⇒ 4x + 7y = 11

⇒ 7y = 11 - 4x

Hence, the equation of the line passing through the given points (1, 1), (8, −3) is 7y = 11 - 4x