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

$x + 2 y = 7$

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.

$2 y = 7 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

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

Remove parentheses.

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

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

$m = - \frac{1}{2}$

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

$m_{parallel} = - \frac{1}{2}$