# Find the value of m so that the lines with equations −3y+2x=4 and mx+2y=3 are perpendicular

Find the value of m so that the lines with equations −3y+2x=4 and mx+2y=3 are perpendicular
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Griffin Dean
Put both equations into the form y=mx+c
$-3y+2x=4$
$3y=2x-4$
$y=\frac{2}{3}x-\frac{4}{3}$
For the 2nd eqn:
$mx+2y=3$
$2y=3-mx$
$y=-\frac{m}{2}x-\frac{3}{2}$
If the lines are perpendicular the product of their gradients = -1
So $-\frac{m}{2}×\frac{2}{3}=-1$
m=3