Question

Find the equation of the line through $(-2,3)$ and perpendicular to the line $2x-3y=4$.

Answer 1

Given equation of line is $2x-3y=4$

The slope of line $2x-3y=4$ is $\frac{2}{3}$.
Therefore, the slope of line perpendicular to given line is $-\frac{3}{2}$
The equation of line passing through $(-2,3)$ is

$y-3=-\frac{3(x+2)}{2}$
$\Rightarrow 2y-6=-3x-6$

$\Rightarrow 3x+2y=0$