Find the Slope of a Perpendicular Line x+8y=6

$x + 8 y = 6$

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.

$8 y = 6 - x$

Divide each term in $8 y = 6 - x$ by $8$ and simplify.

Divide each term in $8 y = 6 - x$ by $8$ .

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

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{8} + \frac{- x}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$y = \frac{2 \cdot 3}{2 \cdot 4} + \frac{- x}{8}$

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 4} + \frac{- x}{8}$

Rewrite the expression.

$y = \frac{3}{4} + \frac{- x}{8}$

Move the negative in front of the fraction.

$y = \frac{3}{4} - \frac{x}{8}$

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

Reorder $\frac{3}{4}$ and $- \frac{x}{8}$ .

$y = - \frac{x}{8} + \frac{3}{4}$

Reorder terms.

$y = - (\frac{1}{8} x) + \frac{3}{4}$

Remove parentheses.

$y = - \frac{1}{8} x + \frac{3}{4}$

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 $y = - \frac{1}{8} x + \frac{3}{4}$ 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.

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

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

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

Move the negative in front of the fraction.

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

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 $8$ .

$m_{perpendicular} = 8$

Multiply $- 1$ by $- 8$ .

$m_{perpendicular} = 8$

Step 5

Find the Slope of a Perpendicular Line x+8y=6

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