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

Nov 30, 2016

The slope of the line is $\frac{1}{2}$

#### Explanation:

The product of the slopes of two perpendicular lines is $- 1$.

The slope of the line $2 x + y = 4 \mathmr{and} y = - 2 x + 4$ is $- 2$ (Compare with y=mx+c)

Let ${m}_{2}$ is the slope of the perpendicular line.
${m}_{2} \cdot \left(- 2\right) = - 1 \therefore {m}_{2} = \frac{1}{2}$

So the slope of the line is $\frac{1}{2}$[Ans]

Nov 30, 2016

Slope of lines perpendicular to $y$ is $\frac{1}{2}$

#### Explanation:

$2 x + y = 4$

$y = - 2 x + 4$

A straight iine in slope $\left(m\right)$ and intercept $\left(c\right)$ form has the equation:
$y = m x + c$

Hence this example $m = - 2$

Lines perpendicular to $y$ will have a slope $\left({m}_{1}\right)$ that satisfies $m \cdot {m}_{1} = - 1$

$\therefore {m}_{1} = - \frac{1}{-} 2 = \frac{1}{2}$