How do you find the slope that is perpendicular to the line 3x + 2y = -6?

Mar 12, 2017

$\text{perpendicular slope } = \frac{2}{3}$

Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$\text{Rearrange " 3x+2y=-6" into this form}$

subtract 3x from both sides.

$\cancel{3 x} \cancel{- 3 x} + 2 y = - 3 x - 6$

$\Rightarrow 2 y = - 3 x - 6$

divide both sides by 2

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

$\Rightarrow y = - \frac{3}{2} x - 2 \leftarrow \text{ in slope-intercept form}$

$\Rightarrow \text{slope } = - \frac{3}{2}$

The slope perpendicular to this is the $\textcolor{b l u e}{\text{negative reciprocal}}$ of m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{3}{2}} = \frac{2}{3}$