# How do you find the slope that is perpendicular to the line 2x + y = 4?

May 18, 2017

$\frac{1}{2}$

#### Explanation:

First set the equation in terms of $y$:

To do this, subtract $2 x$ from both sides:

$\cancel{2 x - 2 x} + y = 4 - 2 x$

$y = 4 - 2 x$

To find the perpendicular slope or $m \bot$ we first must find the slope of the equation given: The slope is the number that is next to the variable and not the constant. The slope($m$) in this case is $- 2$

To find the perpendicular slope algebraically, we use the following: $m \bot = - \frac{1}{m}$ because it is the negative reciprocal of the original slope. We then plug in $- 2$ for $m$:

$m \bot = - \frac{1}{-} 2 = \frac{1}{2}$

$\therefore$ the perpendicular slope is $\frac{1}{2}$