# How do you write an equation of a line passing through (2, -2), perpendicular to y = –x + 3?

Dec 6, 2017

$y = x - 4$

#### Explanation:

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

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

•color(white)(x)y=mx+b

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

$y = - x + 3 \text{ is in this form}$

$\text{with } m = - 1$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{- 1} = 1$

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

$\text{to find b substitute "(2,-2)" into the partial equation}$

$- 2 = 2 + b \Rightarrow b = - 4$

$\Rightarrow y = x - 4 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$