Find the Slope -2x-8y=21

$- 2 x - 8 y = 21$

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 $2 x$ to both sides of the equation.

$- 8 y = 21 + 2 x$

Divide each term in $- 8 y = 21 + 2 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 21 + 2 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{21}{- 8} + \frac{2 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{21}{- 8} + \frac{2 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{21}{- 8} + \frac{2 x}{- 8}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{21}{8} + \frac{2 x}{- 8}$

Cancel the common factor of $2$ and $- 8$ .

Factor $2$ out of $2 x$ .

$y = - \frac{21}{8} + \frac{2 (x)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$y = - \frac{21}{8} + \frac{2 x}{2 \cdot - 4}$

Cancel the common factor.

$y = - \frac{21}{8} + \frac{2 x}{2 \cdot - 4}$

Rewrite the expression.

$y = - \frac{21}{8} + \frac{x}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{21}{8} - \frac{x}{4}$

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

Reorder $- \frac{21}{8}$ and $- \frac{x}{4}$ .

$y = - \frac{x}{4} - \frac{21}{8}$

Reorder terms.

$y = - (\frac{1}{4} x) - \frac{21}{8}$

Remove parentheses.

$y = - \frac{1}{4} x - \frac{21}{8}$

Step 2

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

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

Step 3