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

$2 x + 7 y = 7$

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.

$7 y = 7 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $7$ by $7$ .

$y = 1 + \frac{- 2 x}{7}$

Move the negative in front of the fraction.

$y = 1 - \frac{2 x}{7}$

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

Reorder $1$ and $- \frac{2 x}{7}$ .

$y = - \frac{2 x}{7} + 1$

Reorder terms.

$y = - (\frac{2}{7} x) + 1$

Remove parentheses.

$y = - \frac{2}{7} x + 1$

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

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

All lines that are parallel to $y = - \frac{2}{7} x + 1$ have the same slope of $- \frac{2}{7}$ .

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