# What is the equation of the line that passes through the point (-2,-2) and is perpendicular to y= -1/3x + 9?

Mar 8, 2018

$y = 3 x + 4$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$y = - \frac{1}{3} x + 9 \text{ is in this form}$

$\text{with slope } = m = - \frac{1}{3}$

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

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

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{- \frac{1}{3}} = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$- 2 = - 6 + b \Rightarrow b = - 2 + 6 = 4$

$\Rightarrow y = 3 x + 4 \leftarrow \textcolor{red}{\text{equation of perpendicular line}}$