Question

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is ______.

Options

• `1/3`

• `2/3`

• 1

• `4/3`

Answer 1

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is `4/3`.

Explanation:

Any line perpendicular to 3x + y = 3

x – 3y = λ    ....(λ = constant)

If it passes through the point (2, 2)

Then 2 – 3(2) = λ

⇒ λ = – 4

∴ Required equation is x – 3y = – 4

⇒ – 3y = – x – 4

⇒ y = `1/3x + 4/3`  ......[∵ y = mx + c]

So, the y-intercept is `4/3`.