Find the Slope of a Parallel Line 7x-8y=6

$7 x - 8 y = 6$

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 $7 x$ from both sides of the equation.

$- 8 y = 6 - 7 x$

Divide each term in $- 8 y = 6 - 7 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 6 - 7 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{6}{- 8} + \frac{- 7 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{6}{- 8} + \frac{- 7 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{6}{- 8} + \frac{- 7 x}{- 8}$

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{- 8} + \frac{- 7 x}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$y = \frac{2 \cdot 3}{2 \cdot - 4} + \frac{- 7 x}{- 8}$

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot - 4} + \frac{- 7 x}{- 8}$

Rewrite the expression.

$y = \frac{3}{- 4} + \frac{- 7 x}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{3}{4} + \frac{- 7 x}{- 8}$

Dividing two negative values results in a positive value.

$y = - \frac{3}{4} + \frac{7 x}{8}$

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

Reorder $- \frac{3}{4}$ and $\frac{7 x}{8}$ .

$y = \frac{7 x}{8} - \frac{3}{4}$

Reorder terms.

$y = \frac{7}{8} x - \frac{3}{4}$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{8}$ .

$m = \frac{7}{8}$

Step 3

All lines that are parallel to $y = \frac{7}{8} x - \frac{3}{4}$ have the same slope of $\frac{7}{8}$ .

$m_{parallel} = \frac{7}{8}$

Step 4