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

$x - 8 y = 5$

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.

$y = m x + b$

Subtract $x$ from both sides of the equation.

$- 8 y = 5 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

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

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

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{1}{8}$ .

$m = \frac{1}{8}$

Step 3

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

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 8)$

Multiply $- (1 \cdot 8)$ .

Multiply $8$ by $1$ .

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

Multiply $- 1$ by $8$ .

$m_{perpendicular} = - 8$

Step 5