Find the Slope -3y=2x+7

$- 3 y = 2 x + 7$

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.

$y = m x + b$

Divide each term in $- 3 y = 2 x + 7$ by $- 3$ and simplify.

Divide each term in $- 3 y = 2 x + 7$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{2 x}{- 3} + \frac{7}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{2 x}{- 3} + \frac{7}{- 3}$

Divide $y$ by $1$ .

$y = \frac{2 x}{- 3} + \frac{7}{- 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} + \frac{7}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} - \frac{7}{3}$

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

Reorder terms.

$y = - (\frac{2}{3} x) - \frac{7}{3}$

Remove parentheses.

$y = - \frac{2}{3} x - \frac{7}{3}$

Step 2

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

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

Step 3