Question

Find the equation of the line passing through the point $(2,3)$ and perpendicular to the line $3x+2y-1=0$

Answer 1

The line $3x+2y=1$ is of the form $ax+by=c$

$\Rightarrow$ slope $=\frac{-a}{b}=\frac{-3}{2}$

$\therefore$ slope of the line perpendicular to the line passing through $(2,3)$ is $=\frac{2}{3}$

$\therefore$ equation of line passing through $(2,3)$ is

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

$\Rightarrow 3y-9=2x-4$

$\Rightarrow 2x-3y+5=0$