# What is the slope of a line perpendicular to x+2y=7?

Jul 6, 2018

The slope perpendicular to the equation is 2.

#### Explanation:

First, find the slope of the equation by setting it into slope-intercept form, $y = m x + b$:
$x + 2 y = 7$

Subtract $\textcolor{b l u e}{x}$ from both sides:
$x + 2 y \quad \textcolor{b l u e}{- \quad x} = 7 \quad \textcolor{b l u e}{- \quad x}$

$2 y = 7 - x$

Divide both sides by $\textcolor{b l u e}{2}$:
$\frac{2 y}{\textcolor{b l u e}{2}} = \frac{7 - x}{\textcolor{b l u e}{2}}$

$y = \frac{7}{2} - \frac{1}{2} x$

We know that the slope of a slope-intercept equation is the value multiplied by $x$. That means the slope of the equation is $- \frac{1}{2}$.

Now to find the slope perpendicular to the equation, we find the negative reciprocal, or switching the sign and doing $1$ over the slope.

So:
$\frac{- 1}{- \frac{1}{2}} = - 2$

Therefore, the slope perpendicular to the equation is 2.

Hope this helps!