Question

The equation of the 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

The correct option is A $3x+2y-6=0$

Given equation of line is $2x-3y+5=0$

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 intercepty-axis $=3,$ i.e., $c=3$.
We know $y=mx+c$
Therefore, $y=-\frac{3}{2}x+3$
$\Rightarrow 3x+2y-6=0$