Find the Slope -7x=6+3y

$- 7 x = 6 + 3 y$

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.

$y = m x + b$

Rewrite the equation as $6 + 3 y = - 7 x$ .

$6 + 3 y = - 7 x$

Subtract $6$ from both sides of the equation.

$3 y = - 7 x - 6$

Divide each term in $3 y = - 7 x - 6$ by $3$ and simplify.

Divide each term in $3 y = - 7 x - 6$ by $3$ .

$\frac{3 y}{3} = \frac{- 7 x}{3} + \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 7 x}{3} + \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{- 7 x}{3} + \frac{- 6}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{(7) x}{3} + \frac{- 6}{3}$

Divide $- 6$ by $3$ .

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{7}{3}$ .

$m = - \frac{7}{3}$

Step 3