# What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line x + y = 13?

Jun 8, 2018

$y = - x - 1$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{rearrange "x+y=13" into this form}$

$\text{subtract "x" from both sides}$

$y = - x + 13 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = - 1$

• " Parallel lines have equal slopes"

$y = - x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-8,7)" into the partial equation}$

$7 = 8 + b \Rightarrow b = 7 - 8 = - 1$

$y = - x - 1 \leftarrow \textcolor{red}{\text{slope-intercept form of parallel line}}$