Write in y=mx+b Form 3x+7y=4y-2

$3 x + 7 y = 4 y - 2$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Move all terms containing $y$ to the left side of the equation.

Subtract $4 y$ from both sides of the equation.

$3 x + 7 y - 4 y = - 2$

Subtract $4 y$ from $7 y$ .

$3 x + 3 y = - 2$

Subtract $3 x$ from both sides of the equation.

$3 y = - 2 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3 x$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - \frac{2}{3} + \frac{3 (- x)}{3 (1)}$

Cancel the common factor.

$y = - \frac{2}{3} + \frac{3 (- x)}{3 \cdot 1}$

Rewrite the expression.

$y = - \frac{2}{3} + \frac{- x}{1}$

Divide $- x$ by $1$ .

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

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

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