Write in y=mx+b Form 2x-2(x+2)=3y-2x

$2 x - 2 (x + 2) = 3 y - 2 x$

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.

Simplify the left side.

Simplify $2 x - 2 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$2 x - 2 x - 2 \cdot 2 = 3 y - 2 x$

Multiply $- 2$ by $2$ .

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

Simplify by adding terms.

Subtract $2 x$ from $2 x$ .

$0 - 4 = 3 y - 2 x$

Subtract $4$ from $0$ .

$- 4 = 3 y - 2 x$

Rewrite the equation as $3 y - 2 x = - 4$ .

$3 y - 2 x = - 4$

Add $2 x$ to both sides of the equation.

$3 y = - 4 + 2 x$

Divide each term in $3 y = - 4 + 2 x$ by $3$ and simplify.

Divide each term in $3 y = - 4 + 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 4}{3} + \frac{2 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 4}{3} + \frac{2 x}{3}$

Divide $y$ by $1$ .

$y = \frac{- 4}{3} + \frac{2 x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{4}{3} + \frac{2 x}{3}$

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

Reorder $- \frac{4}{3}$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - \frac{4}{3}$

Reorder terms.

$y = \frac{2}{3} x - \frac{4}{3}$