# What is the equation of the line perpendicular to y=-1/5x  that passes through  (7,4) ?

Dec 23, 2015

$5 x - y = 31$

#### Explanation:

$y = - \frac{1}{5} x$ has a slope of $\left(- \frac{1}{5}\right)$
all line perpendicular to this will have a slope of $5$
(if a line has a slope of $m$, lines perpendicular to it have a slope of $\left(- \frac{1}{m}\right)$)

If a line has a slope $m = 5$ and passes through the point $\left(\overline{x} , \overline{y}\right) = \left(7 , 4\right)$
then we can write the equation of this line in "slope-point" form as
$\textcolor{w h i t e}{\text{XXX}} \left(y - \overline{y}\right) = m \left(x - \overline{x}\right)$

In this case
$\textcolor{w h i t e}{\text{XXX}} \left(y - 4\right) = 5 \left(x - 7\right)$

While this is a valid answer to the given question, let's convert it into standard form: $a x + b y = c$ with a,b,c in ZZ; a>=0

$\textcolor{w h i t e}{\text{XXX}} y - 4 = 5 x - 35$

$\textcolor{w h i t e}{\text{XXX}} 5 x - y = 31$