Find the Slope 3(y-1)=2x+2

$3 (y - 1) = 2 x + 2$

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.

$y = m x + b$

Simplify the left side.

Simplify $3 (y - 1)$ .

Apply the distributive property.

$3 y + 3 \cdot - 1 = 2 x + 2$

Multiply $3$ by $- 1$ .

$3 y - 3 = 2 x + 2$

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

Add $3$ to both sides of the equation.

$3 y = 2 x + 2 + 3$

Add $2$ and $3$ .

$3 y = 2 x + 5$

Divide each term in $3 y = 2 x + 5$ by $3$ and simplify.

Divide each term in $3 y = 2 x + 5$ by $3$ .

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{5}{3}$

Divide $y$ by $1$ .

$y = \frac{2 x}{3} + \frac{5}{3}$

Reorder terms.

$y = \frac{2}{3} x + \frac{5}{3}$

Step 2

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

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

Step 3