Find the Slope of a Perpendicular Line x-4y=6

$x - 4 y = 6$

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.

$- 4 y = 6 - x$

Divide each term in $- 4 y = 6 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 6 - x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{6}{- 4} + \frac{- x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{6}{- 4} + \frac{- x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{6}{- 4} + \frac{- x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{- 4} + \frac{- x}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

Reorder $- \frac{3}{2}$ and $\frac{x}{4}$ .

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

Reorder terms.

$y = \frac{1}{4} x - \frac{3}{2}$

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 $y = \frac{1}{4} x - \frac{3}{2}$ 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.

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 $4$ .

$m_{perpendicular} = - 4$

Step 5

Find the Slope of a Perpendicular Line x-4y=6

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