# How you find the value of m so that the lines with equations -3y+2x=4 and mx + 2y = 3 are perpendicular?

Feb 5, 2015

$m = 3$

Put both equations into the form $y = m x + c$

$- 3 y + 2 x = 4$

$3 y = 2 x - 4$

$y = \frac{2}{3} x - \frac{4}{3}$

For the 2nd eqn:

$m x + 2 y = 3$

$2 y = 3 - m x$

$y = - \frac{m}{2} x - \frac{3}{2}$

If the lines are perpendicular the product of their gradients = -1

So $- \frac{m}{2} \times \frac{2}{3} = - 1$

$m = 3$