Find the Slope of a Parallel Line 2y=3x+5

$2 y = 3 x + 5$

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 $2 y = 3 x + 5$ by $2$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Reorder terms.

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

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

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

All lines that are parallel to $y = \frac{3}{2} x + \frac{5}{2}$ have the same slope of $\frac{3}{2}$ .

$m_{parallel} = \frac{3}{2}$