Find the Slope and y-intercept 2y=3x+12

$2 y = 3 x + 12$

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.

$y = m x + b$

Divide each term in $2 y = 3 x + 12$ by $2$ and simplify.

Divide each term in $2 y = 3 x + 12$ by $2$ .

$\frac{2 y}{2} = \frac{3 x}{2} + \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{3 x}{2} + \frac{12}{2}$

Divide $y$ by $1$ .

$y = \frac{3 x}{2} + \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$y = \frac{3 x}{2} + 6$

Reorder terms.

$y = \frac{3}{2} x + 6$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

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

$b = 6$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{3}{2}$

y-intercept: $(0, 6)$

Slope: $\frac{3}{2}$

y-intercept: $(0, 6)$

Step 3