# How do you find the slope that is perpendicular to the line 3x-2y=7?

Jun 20, 2016

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

#### Explanation:

First, write the equation in standard form, $y = m x + c$

$2 y = 3 x - 7$

y = 3/2x - 3½

The gradient of this line is $\frac{3}{2}$

The slope perpendicular to this is $- \frac{2}{3}$

The one is the negative reciprocal of the other.

${m}_{1} \times {m}_{2} = - 1$

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

Jun 20, 2016

Reqd. slope $= - \frac{2}{3.}$

#### Explanation:

We write the given eqn. of line as $3 x - 7 = 2 y ,$ or, $y = \frac{3}{2} x - \frac{7}{2}$, giving its slope$= \frac{3}{2.}$

Hence, the slope of a line perp. to this is $- \frac{1}{\frac{3}{2}} = - \frac{2}{3.}$