A line is perpendicular to \(3x - y + 11 = 0\) and passes through the point (1, -5). Find its equation.

A.

3y - x -14 = 0

B.

3x + y + 1 = 0

C.

3y + x + 1 = 0

D.

3y + x + 14 = 0

Correct answer is D

\(3x - y + 11 = 0 \implies y = 3x + 11\)

\(Gradient = 3\)

Gradient of perpendicular line = \(\frac{-1}{3}\)

\(\therefore \frac{y - (-5)}{x - 1} = \frac{-1}{3}\)

\(3(y + 5) = 1 - x\)

\(3y + x + 15 - 1 = 3y + x + 14 = 0\)