# Question #06e3a

Nov 11, 2017

The line perpendicular to the given line is
$y + 2 = 5 \left(x - 3\right)$
or
$y = 5 x - 17$

#### Explanation:

You are given a point and an easy way to find slope, so the most convenient equation is the point-slope form of the equation of the wanted line.

Find the slope of the wanted line
The slopes of lines that are perpendicular to each other are the "negative inverse" of each other's slopes.

So first, find the slope of the given line by solving for $y$
$x + 5 y = 1$

Subtract $x$ from both sides to isolate the $5 y$ term
$5 y = - 1 x + 1$

Divide both sides by $5$ to isolate $y$
$y = \left(- \frac{1}{5}\right) x + \frac{1}{5}$

The slope of the given line is $- \frac{1}{5}$
......................

The slope of any line perpendicular to this one is
the "negative inverse" of $- \frac{1}{5}$
The negative inverse is $+ 5$
So the slope of the wanted line is $5$
.......................

The point-slope formula of a line is
$y - b = m \left(x - a\right)$
where $\left(a , b\right)$ is the ordered pair of the given point

Subbing in $5$ for $m$, and (3,-2) for $\left(a , b\right)$ gives you the equation
for the wanted line
$y - b = m \left(x - a\right)$
$y - \left(- 2\right) = 5 \left(x - 3\right)$

This simplifies to
$y + 2 = 5 \left(x - 3\right)$

$y + 2 = 5 \left(x - 3\right)$
$y = 5 x - 17$ ← same answer