Find the Slope of a Parallel Line 7x-2y=6

$7 x - 2 y = 6$

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.

$- 2 y = 6 - 7 x$

Divide each term in $- 2 y = 6 - 7 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 6 - 7 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 7 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 7 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{6}{- 2} + \frac{- 7 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

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

Reorder $- 3$ and $\frac{7 x}{2}$ .

$y = \frac{7 x}{2} - 3$

Reorder terms.

$y = \frac{7}{2} x - 3$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{2}$ .

$m = \frac{7}{2}$

Step 3

All lines that are parallel to $y = \frac{7}{2} x - 3$ have the same slope of $\frac{7}{2}$ .

$m_{parallel} = \frac{7}{2}$

Step 4