# What is the equation of the line in slope-intercept form that passes through the point (3, –5) and is perpendicular to y = –3x – 4?

Sep 9, 2017

$y = \frac{1}{3} x - 6$

#### Explanation:

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

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

$y = - 3 x - 4 \text{ is in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

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

$\Rightarrow y = - 3 x - 4 \text{ has slope } m = - 3$

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

$\Rightarrow y = \frac{1}{3} x + b \leftarrow \text{ partial equation}$

$\text{to find b substitute "(3,-5)" into the partial equation}$

$- 5 = 1 + b \Rightarrow b = - 6$

$\Rightarrow y = \frac{1}{3} x - 6 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$