Question

The equation of a line passing through (2, 1) and perpendicular to the line 3x − 4y = 8 is ______.

Options

• 4x + 3y = 11

• 4x + 3y = 8

• 3x − 4y = 11

• 3x + 4y = 10

Answer 1

The equation of a line passing through (2, 1) and perpendicular to the line 3x − 4y = 8 is 4x + 3y = 11.

Explanation:

To get a line perpendicular to 3x − 4y = 8,

Now, swap the x and y coefficients, and also change the sign between them.

The form becomes: 4x + 3y = k

Let’s solve for k:

Substitute the point (2, 1) into the new equation:

4(2) + 3(1) = k

8 + 3 = k

∴ k  = 11

Putting it all together, we get 4x + 3y = 11.