Question

The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is
(a) 5x + 3y − 20 = 0
(b) 3x − 5y + 7 = 0
(c) 3x − 5y + 6 = 0
(d) 5x + 3y + 7 = 0

Answer 1

(a) $5x+3y-20=0$

A line perpendicular to 3x − 5y + 7 = 0 is given by

$5x+3y+\lambda =0$

This line passes through (1, 5).

$$\begin{gathered} 5+15+\lambda =0 \\ \Rightarrow \lambda =-20 \end{gathered}$$

Therefore, the equation of the required line is $5x+3y-20=0$