How do you find the slope and y-intercept of the graph of 2x + 4y=-8?

Sep 4, 2016

slope $= - \frac{1}{2}$
y-intercept = - 2

Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b can be extracted 'easily'.

Rearrange $2 x + 4 y = - 8 \text{ into this form}$

subtract 2x from both sides of the equation.

$\Rightarrow \cancel{2 x} - \cancel{2 x} + 4 y = - 8 - 2 x \Rightarrow 4 y = - 2 x - 8$

now divide both sides by 4 to obtain y.

$\Rightarrow \frac{{\cancel{4}}^{1} y}{\cancel{4}} ^ 1 = \frac{{\cancel{- 2}}^{-} 1}{\cancel{4}} ^ 2 x - {\cancel{8}}^{2} / {\cancel{4}}^{1}$

$\Rightarrow y = - \frac{1}{2} x - 2 \text{ is equation in y = mx + b form}$

from this $\text{slope" =-1/2" and y-intercept} = - 2$