Find the Slope of a Parallel Line 6x+7y=3

$6 x + 7 y = 3$

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 $6 x$ from both sides of the equation.

$7 y = 3 - 6 x$

Divide each term in $7 y = 3 - 6 x$ by $7$ and simplify.

Divide each term in $7 y = 3 - 6 x$ by $7$ .

$\frac{7 y}{7} = \frac{3}{7} + \frac{- 6 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{3}{7} + \frac{- 6 x}{7}$

Divide $y$ by $1$ .

$y = \frac{3}{7} + \frac{- 6 x}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3}{7} - \frac{6 x}{7}$

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

Reorder $\frac{3}{7}$ and $- \frac{6 x}{7}$ .

$y = - \frac{6 x}{7} + \frac{3}{7}$

Reorder terms.

$y = - (\frac{6}{7} x) + \frac{3}{7}$

Remove parentheses.

$y = - \frac{6}{7} x + \frac{3}{7}$

Step 2

Using the slope-intercept form, the slope is $- \frac{6}{7}$ .

$m = - \frac{6}{7}$

Step 3

All lines that are parallel to $y = - \frac{6}{7} x + \frac{3}{7}$ have the same slope of $- \frac{6}{7}$ .

$m_{parallel} = - \frac{6}{7}$

Step 4