Write in y=mx+b Form 2(y-3)=2x-6

$2 (y - 3) = 2 x - 6$

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 in slope-intercept form.

Simplify the left side.

Simplify $2 (y - 3)$ .

Apply the distributive property.

$2 y + 2 \cdot - 3 = 2 x - 6$

Multiply $2$ by $- 3$ .

$2 y - 6 = 2 x - 6$

Move all terms not containing $y$ to the right side of the equation.

Add $6$ to both sides of the equation.

$2 y = 2 x - 6 + 6$

Combine the opposite terms in $2 x - 6 + 6$ .

Add $- 6$ and $6$ .

$2 y = 2 x + 0$

Add $2 x$ and $0$ .

$2 y = 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$y = x$