Find the Slope of a Parallel Line 6x-8y=3

$6 x - 8 y = 3$

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 $6 x$ from both sides of the equation.

$- 8 y = 3 - 6 x$

Divide each term in $- 8 y = 3 - 6 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 3 - 6 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{3}{8} + \frac{- 6 x}{- 8}$

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6 x$ .

$y = - \frac{3}{8} + \frac{- 2 (3 x)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$y = - \frac{3}{8} + \frac{- 2 (3 x)}{- 2 (4)}$

Cancel the common factor.

$y = - \frac{3}{8} + \frac{- 2 (3 x)}{- 2 \cdot 4}$

Rewrite the expression.

$y = - \frac{3}{8} + \frac{3 x}{4}$

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

Reorder $- \frac{3}{8}$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} - \frac{3}{8}$

Reorder terms.

$y = \frac{3}{4} x - \frac{3}{8}$

Using the slope-intercept form, the slope is $\frac{3}{4}$ .

$m = \frac{3}{4}$

All lines that are parallel to $y = \frac{3}{4} x - \frac{3}{8}$ have the same slope of $\frac{3}{4}$ .

$m_{parallel} = \frac{3}{4}$