Find the Slope of a Parallel Line 2x+9y=4

$2 x + 9 y = 4$

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 $2 x$ from both sides of the equation.

$9 y = 4 - 2 x$

Divide each term in $9 y = 4 - 2 x$ by $9$ and simplify.

Divide each term in $9 y = 4 - 2 x$ by $9$ .

$\frac{9 y}{9} = \frac{4}{9} + \frac{- 2 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{4}{9} + \frac{- 2 x}{9}$

Divide $y$ by $1$ .

$y = \frac{4}{9} + \frac{- 2 x}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{4}{9} - \frac{2 x}{9}$

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

Reorder $\frac{4}{9}$ and $- \frac{2 x}{9}$ .

$y = - \frac{2 x}{9} + \frac{4}{9}$

Reorder terms.

$y = - (\frac{2}{9} x) + \frac{4}{9}$

Remove parentheses.

$y = - \frac{2}{9} x + \frac{4}{9}$

Step 2

Using the slope-intercept form, the slope is $- \frac{2}{9}$ .

$m = - \frac{2}{9}$

Step 3

All lines that are parallel to $y = - \frac{2}{9} x + \frac{4}{9}$ have the same slope of $- \frac{2}{9}$ .

$m_{parallel} = - \frac{2}{9}$

Step 4