Find the Slope of a Parallel Line -7x-4y=-4

$- 7 x - 4 y = - 4$

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 $7 x$ to both sides of the equation.

$- 4 y = - 4 + 7 x$

Divide each term in $- 4 y = - 4 + 7 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 4 + 7 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4} + \frac{7 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4} + \frac{7 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 4} + \frac{7 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $- 4$ by $- 4$ .

$y = 1 + \frac{7 x}{- 4}$

Move the negative in front of the fraction.

$y = 1 - \frac{7 x}{4}$

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

Reorder $1$ and $- \frac{7 x}{4}$ .

$y = - \frac{7 x}{4} + 1$

Reorder terms.

$y = - (\frac{7}{4} x) + 1$

Remove parentheses.

$y = - \frac{7}{4} x + 1$

Step 2

Using the slope-intercept form, the slope is $- \frac{7}{4}$ .

$m = - \frac{7}{4}$

Step 3

All lines that are parallel to $y = - \frac{7}{4} x + 1$ have the same slope of $- \frac{7}{4}$ .

$m_{parallel} = - \frac{7}{4}$

Step 4