Find the Slope of a Parallel Line 4x-9y=5

$4 x - 9 y = 5$

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 $4 x$ from both sides of the equation.

$- 9 y = 5 - 4 x$

Divide each term in $- 9 y = 5 - 4 x$ by $- 9$ and simplify.

Divide each term in $- 9 y = 5 - 4 x$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Divide $y$ by $1$ .

$y = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5}{9} + \frac{- 4 x}{- 9}$

Dividing two negative values results in a positive value.

$y = - \frac{5}{9} + \frac{4 x}{9}$

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

Reorder $- \frac{5}{9}$ and $\frac{4 x}{9}$ .

$y = \frac{4 x}{9} - \frac{5}{9}$

Reorder terms.

$y = \frac{4}{9} x - \frac{5}{9}$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{9}$ .

$m = \frac{4}{9}$

Step 3

All lines that are parallel to $y = \frac{4}{9} x - \frac{5}{9}$ have the same slope of $\frac{4}{9}$ .

$m_{parallel} = \frac{4}{9}$

Step 4