Find the Slope of a Parallel Line -4x-3y=7

$- 4 x - 3 y = 7$

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 $4 x$ to both sides of the equation.

$- 3 y = 7 + 4 x$

Divide each term in $- 3 y = 7 + 4 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 7 + 4 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{7}{- 3} + \frac{4 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{7}{- 3} + \frac{4 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{7}{- 3} + \frac{4 x}{- 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{7}{3} + \frac{4 x}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{7}{3} - \frac{4 x}{3}$

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

Reorder $- \frac{7}{3}$ and $- \frac{4 x}{3}$ .

$y = - \frac{4 x}{3} - \frac{7}{3}$

Reorder terms.

$y = - (\frac{4}{3} x) - \frac{7}{3}$

Remove parentheses.

$y = - \frac{4}{3} x - \frac{7}{3}$

Step 2

Using the slope-intercept form, the slope is $- \frac{4}{3}$ .

$m = - \frac{4}{3}$

Step 3

All lines that are parallel to $y = - \frac{4}{3} x - \frac{7}{3}$ have the same slope of $- \frac{4}{3}$ .

$m_{parallel} = - \frac{4}{3}$

Step 4