# How do you write the slope-intercept equation for the line that is parallel to the graph of:x+y=6 and passes through (1,-4)?

Jun 1, 2018

$y = - x - 3$

#### Explanation:

• " Parallel lines have equal slopes"

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

•color(white)(x)y=mx+b

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

$\text{rearrange "x+y=6" into this form}$

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

$y = - x + 6 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope m } = - 1$

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

$\text{to find b substitute "(1,-4)" into the partial equation}$

$- 4 = - 1 + b \Rightarrow b = - 4 + 1 = - 3$

$y = - x - 3 \leftarrow \textcolor{red}{\text{equation in slope-intercept form}}$