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

$x + 3 y = 7$

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 $x$ from both sides of the equation.

$3 y = 7 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{7}{3}$

Remove parentheses.

$y = - \frac{1}{3} x + \frac{7}{3}$

Using the slope-intercept form, the slope is $- \frac{1}{3}$ .

$m = - \frac{1}{3}$

All lines that are parallel to $y = - \frac{1}{3} x + \frac{7}{3}$ have the same slope of $- \frac{1}{3}$ .

$m_{parallel} = - \frac{1}{3}$