# Whats the slope of a line perpendicular to x - y = 16?

Jul 22, 2015

All lines perpendicular to $x - y = 16$
have a slope of $- 1$

#### Explanation:

$x - y = 16$ has a slope of $1$
$\textcolor{w h i t e}{\text{XXXX}}$(this can be demonstrated by:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\circ$ converting to slope-point form
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$or
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\circ$ using the slope $= - \frac{b}{a}$ formula)

If a line has a slope of $m$
$\textcolor{w h i t e}{\text{XXXX}}$all lines perpendicular to it have a slope of $\left(- \frac{1}{m}\right)$

Therefore all lines perpendicular to $x - y = 16$
$\textcolor{w h i t e}{\text{XXXX}}$have a slope of $\left(- 1\right)$