# How do you find the slope and intercept of 5x + 2y = 10?

Aug 3, 2016

slope $= - \frac{5}{2}$
y-intercept = 5

#### 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 may be extracted 'easily'

Rearrange 5x + 2y = 10 into this form.

subtract 5x from both sides

$\cancel{5 x} + 2 y \cancel{- 5 x} = 10 - 5 x \Rightarrow 2 y = - 5 x + 10$

now divide both sides by 2

$\frac{{\cancel{2}}^{1} y}{\cancel{2}} ^ 1 = \frac{- 5}{2} x + \frac{10}{2} \Rightarrow \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = - \frac{5}{2} x + 5} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \text{ slope" =-5/2" and y-intercept} = 5$