Find the Slope of a Parallel Line 3x+8y=3

$3 x + 8 y = 3$

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.

$8 y = 3 - 3 x$

Divide each term in $8 y = 3 - 3 x$ by $8$ and simplify.

Divide each term in $8 y = 3 - 3 x$ by $8$ .

$\frac{8 y}{8} = \frac{3}{8} + \frac{- 3 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{3}{8} + \frac{- 3 x}{8}$

Divide $y$ by $1$ .

$y = \frac{3}{8} + \frac{- 3 x}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3}{8} - \frac{3 x}{8}$

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

Reorder $\frac{3}{8}$ and $- \frac{3 x}{8}$ .

$y = - \frac{3 x}{8} + \frac{3}{8}$

Reorder terms.

$y = - (\frac{3}{8} x) + \frac{3}{8}$

Remove parentheses.

$y = - \frac{3}{8} x + \frac{3}{8}$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{8}$ .

$m = - \frac{3}{8}$

Step 3

All lines that are parallel to $y = - \frac{3}{8} x + \frac{3}{8}$ have the same slope of $- \frac{3}{8}$ .

$m_{parallel} = - \frac{3}{8}$

Step 4