Question

find the equation of the line perpendicular to the line 2x - 3 Y + 12 = 0 and having y intercept -2​

Answer 1

Answer:

The answer is $3x+2y+4=0$

Step-by-step explanation:

We know that slope of line $ax+by+c=0$ is $-\dfrac{a}{b}$

So the slope of line $2x-3y+12=0$ is $-\dfrac{2}{(-3)}=\dfrac{2}{3}$

Let slope of required line is $m$

Also we know that, product of slopes of two perpendicular lines is $-1$

 $\Rightarrow m\times \dfrac{2}{3}=-1\Rightarrow m=-\dfrac{3}{2}$

Therefore using slope intercept form, equation of required line is

                           $y=mx+c$

                         $\Rightarrow y=-\dfrac{3}{2}x-2\\\Rightarrow 2y=-3x-4\\\Rightarrow 3x+2y+4=0$