Find the Slope of a Perpendicular Line -5x-4y=2

$- 5 x - 4 y = 2$

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.

$- 4 y = 2 + 5 x$

Divide each term in $- 4 y = 2 + 5 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 2 + 5 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{5 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{5 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{2}{- 4} + \frac{5 x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4} + \frac{5 x}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{5 x}{- 4}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{5 x}{- 4}$

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{5 x}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{5 x}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} - \frac{5 x}{4}$

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

Reorder $- \frac{1}{2}$ and $- \frac{5 x}{4}$ .

$y = - \frac{5 x}{4} - \frac{1}{2}$

Reorder terms.

$y = - (\frac{5}{4} x) - \frac{1}{2}$

Remove parentheses.

$y = - \frac{5}{4} x - \frac{1}{2}$

Step 2

Using the slope-intercept form, the slope is $- \frac{5}{4}$ .

$m = - \frac{5}{4}$

Step 3

The equation of a perpendicular line to $y = - \frac{5}{4} x - \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{5}{4}}$

Step 4

Simplify the result.

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

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

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{5}{4}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{5}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{4}{5})$

Multiply $\frac{4}{5}$ by $1$ .

$m_{perpendicular} = \frac{4}{5}$

Multiply $- - \frac{4}{5}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{4}{5})$

Multiply $\frac{4}{5}$ by $1$ .

$m_{perpendicular} = \frac{4}{5}$

Step 5

Find the Slope of a Perpendicular Line -5x-4y=2

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