What is the equation of a line that passes through the points (3, 6) and (8, 4)?

Solution:

The equation of the line passing through two points can be found by using two point form of straight lines.

(x - x₁) / (x₂ - x₁) = (y - y₁) / (y₂ - y₁)

Given, two points are (3, 6) and (8, 4).

The equation becomes,

⇒ (x - 3)/(8 - 3) = (y - 6)/(4 - 6)

By further calculation

⇒ (x - 3)/(5) = (y - 6)/(-2)

⇒ (-2)(x - 3) = (5)(y - 6)

Using the multiplicative distributive property

⇒ -2x + 6 = 5y - 30

⇒ 2x + 5y - 36 = 0

Therefore, the equation of the line is 2x + 5y - 36 = 0.

What is the equation of a line that passes through the points (3, 6) and (8, 4)?

Summary:

The equation of a line that passes through the points (3, 6) and (8, 4) is 2x + 5y - 36 = 0.