Find the Slope of a Perpendicular Line x+4y=8

$x + 4 y = 8$

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.

$y = m x + b$

Subtract $x$ from both sides of the equation.

$4 y = 8 - x$

Divide each term in $4 y = 8 - x$ by $4$ and simplify.

Divide each term in $4 y = 8 - x$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $8$ by $4$ .

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

Move the negative in front of the fraction.

$y = 2 - \frac{x}{4}$

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

Reorder $2$ and $- \frac{x}{4}$ .

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

Reorder terms.

$y = - (\frac{1}{4} x) + 2$

Remove parentheses.

$y = - \frac{1}{4} x + 2$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{4}$ .

$m = - \frac{1}{4}$

Step 3

The equation of a perpendicular line to $y = - \frac{1}{4} x + 2$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{1}{4}}$

Step 4

Simplify the result.

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

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

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{1}{4}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 \cdot 4$

Multiply $- - (1 \cdot 4)$ .

Multiply $4$ by $1$ .

$m_{perpendicular} = - (- 1 \cdot 4)$

Multiply $- 1$ by $4$ .

$m_{perpendicular} = 4$

Multiply $- 1$ by $- 4$ .

$m_{perpendicular} = 4$

Step 5

Find the Slope of a Perpendicular Line x+4y=8

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