# What is the slope of the line perpendicular to 2x - 3y - 5 = 0?

Mar 24, 2017

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

#### Explanation:

$\text{rearrange " 2x-3y-5=0" into " color(blue)"slope-intercept form}$

• y=mx+b

where m represents the slope and b, the y-intercept.

$\Rightarrow - 3 y = - 2 x + 5$

divide all terms by - 3

$\frac{\cancel{- 3} y}{\cancel{- 3}} = \frac{- 2}{- 3} x + \frac{5}{- 3}$

$\Rightarrow y = \frac{2}{3} x - \frac{5}{3} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

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

The slope of a perpendicular line is the $\textcolor{b l u e}{\text{negative reciprocal"" of }} m$

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