Find the Slope of a Perpendicular Line -5x-8y=8

$- 5 x - 8 y = 8$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Add $5 x$ to both sides of the equation.

$- 8 y = 8 + 5 x$

Divide each term in $- 8 y = 8 + 5 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 8 + 5 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{8}{- 8} + \frac{5 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{8}{- 8} + \frac{5 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{8}{- 8} + \frac{5 x}{- 8}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 8$ .

$y = - 1 + \frac{5 x}{- 8}$

Move the negative in front of the fraction.

$y = - 1 - \frac{5 x}{8}$

Write in $y = m x + b$ form.

Reorder $- 1$ and $- \frac{5 x}{8}$ .

$y = - \frac{5 x}{8} - 1$

Reorder terms.

$y = - (\frac{5}{8} x) - 1$

Remove parentheses.

$y = - \frac{5}{8} x - 1$

Step 2

Using the slope-intercept form, the slope is $- \frac{5}{8}$ .

$m = - \frac{5}{8}$

Step 3

The equation of a perpendicular line to $y = - \frac{5}{8} x - 1$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{5}{8}}$

Step 4

Simplify the result.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{5}{8}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{5}{8}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{8}{5})$

Multiply $\frac{8}{5}$ by $1$ .

$m_{perpendicular} = \frac{8}{5}$

Multiply $- - \frac{8}{5}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{8}{5})$

Multiply $\frac{8}{5}$ by $1$ .

$m_{perpendicular} = \frac{8}{5}$

Step 5

Find the Slope of a Perpendicular Line -5x-8y=8

Related Questions

Support LCMGCF.com by disabling your adblocker.