Find the Slope of a Parallel Line 2x+3y=-2

$2 x + 3 y = - 2$

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.

$y = m x + b$

Subtract $2 x$ from both sides of the equation.

$3 y = - 2 - 2 x$

Divide each term in $3 y = - 2 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = - 2 - 2 x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{2}{3}$ .

$m = - \frac{2}{3}$

Step 3

All lines that are parallel to $y = - \frac{2}{3} x - \frac{2}{3}$ have the same slope of $- \frac{2}{3}$ .

$m_{parallel} = - \frac{2}{3}$

Step 4