# How do you find the slope that is perpendicular to the line -6x -8y = 8?

Aug 4, 2016

$= \frac{4}{3}$

#### Explanation:

$y = m x + c$ where $m$ is the slope
$- 6 x - 8 y = 8$
or
$8 y = - 6 x - 8$
or
$y = - 6 \frac{x}{8} - \frac{8}{8}$
or
$y = - 3 \frac{x}{4} - 1$
So the slope is $m = - \frac{3}{4}$ of the above lineSo the slope of the line that is perpendicular to the above line$= m 1 = - \frac{1}{m} = \frac{4}{3}$

Aug 4, 2016

${m}_{2} = \frac{4}{3}$

#### Explanation:

$- 6 x - 8 y = 8$

$\text{rearrange the equation -6x-8y=8 as :}$

$8 y = - 6 x - 8$

$y = - \frac{6}{8} x - \frac{8}{8}$

$y = \textcolor{red}{- \frac{3}{4}} x - 1$

$\text{slope of the line is } - \frac{3}{4}$

$\text{the lines are perpendicular if product of their slopes are equal to -1}$

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

$- \frac{3}{4} \cdot {m}_{2} = - 1$

${m}_{2} = \frac{4}{3}$