Question

The equation of the line perpendicular to the line $2x - 3y + 5 = 0$ and making an intercept $3$ with $y$-axis is

• A. 3x + 2y - 6 = 0
• B. 3x + 2y- 12 = 0
• C. 3x - 2y - 6 = 0
• D. 3x + 2y + 6 = 0
• E. 3x + 2y - 5 = 0

Answer 1

Answer: (A)

The slope of the given line is $\frac{2}{3}$.
$\therefore $ The slope of the perpendicular to the given line is $m=-\frac{3}{2}$.
Also, line intercept $y$ -axis $=3$, i.e., $c=3$
$\because y=m x+c$
$\therefore y=-\frac{3}{2} x+3$
$\Rightarrow 3 x+2 y-6=0$