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

$3 x - 2 y = - 5$

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.

$y = m x + b$

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 5 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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

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

Reorder $\frac{5}{2}$ and $\frac{3 x}{2}$ .

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

Reorder terms.

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

Step 2

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

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

Step 3

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

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

Step 4