First write the equation in the standard form of y=mx+c
3x-2y+4=0
3x+4=2y
( divide by 2)
3/2x+2=y
Now let’s find the perpendicular line to y=3/2x+2
You just have to get the opposite of the slope 3/2 which is -2/3
If you multiply 3/2 by -2/3 you will get -1 this proofs it really is the perpendicular slope your are looking for
Hence
The equation of line L is
y=-2/3+2
