# What is the slope of a line that is perpendicular to 3y+2x=6?

Apr 2, 2018

$m = \frac{3}{2}$

#### Explanation:

A line is a negative inverse of it perpendicular line.
This means m(1) $m \left(1\right) = - \frac{1}{m \left(2\right)}$

Through manipulation of the equation we change it to $y = - \frac{2}{3} x + \frac{6}{3}$
The $- \frac{2}{3}$ infront of the represents the slope of the line.
Using idea from earlier we flip the gradient and times it by -1.
$- \frac{2}{3} = - \frac{1}{m}$ (cross multiply)

$3 m = 2$ (divide the 3)

$m = \frac{3}{2}$

Apr 2, 2018

$\frac{3}{2}$

#### Explanation:

If two lines are perpendicular then the result of multiplying the two gradients together always equals -1

Rearrange the equation to find the gradient:

$3 y + 2 x = 6$

$\implies$ $3 y = - 2 x + 6$

$\implies$ $y = - \frac{2}{3} x + 2$

Gradient = $- \frac{2}{3}$ the reciprocal is $\frac{3}{2}$

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