# How do you find the slope and y-intercept of the graph of 2x - 5y= 20?

Mar 3, 2018

See a solution process below:

#### Explanation:

We can convert this equation to slope intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$2 x - 5 y = 20$

$- \textcolor{red}{2 x} + 2 x - 5 y = - \textcolor{red}{2 x} + 20$

$0 - 5 y = - 2 x + 20$

$- 5 y = - 2 x + 20$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{- 2 x + 20}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\cancel{\textcolor{red}{- 5}}} = \frac{- 2 x}{\textcolor{red}{- 5}} + \frac{20}{\textcolor{red}{- 5}}$

$y = \frac{2}{5} x + \left(- 4\right)$

$y = \textcolor{red}{\frac{2}{5}} x - \textcolor{b l u e}{4}$

Therefore:

• The slope is: $\textcolor{red}{m = \frac{2}{5}}$

• The $y$-intercept is: $\textcolor{b l u e}{- 4}$ or $\left(0 , \textcolor{b l u e}{- 4}\right)$