# How do you find the equation of line through point (-6, -1) perpendicular to line 5x-3y=2?

Dec 20, 2017

$y = - \frac{3}{5} x - \frac{23}{5}$

#### Explanation:

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

•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

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

$\text{rearrange "5x-3y=2" into this form}$

$\Rightarrow y = \frac{5}{3} x - \frac{2}{3} \leftarrow \text{ with } m = \frac{5}{3}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{\frac{5}{3}} = - \frac{3}{5}$

$\Rightarrow y = - \frac{3}{5} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute } \left(- 6 , - 1\right)$
$\text{into the partial equation}$

$- 1 = \frac{18}{5} + b \Rightarrow b = - \frac{23}{5}$

$\Rightarrow y = - \frac{3}{5} x - \frac{23}{5} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$