# How do you find the slope and intercept of 4x + 7y = 28?

May 26, 2016

slope $= - \frac{4}{7}$
y-intercept = 4

#### 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 is 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'.

now rearrange 4x + 7y = 28 into this form.

hence : 7y = -4x+28

divide both sides by 7

$\frac{\cancel{7} y}{\cancel{7}} = \frac{- 4}{7} x + \frac{{\cancel{28}}^{4}}{\cancel{7}} ^ 1$

$\Rightarrow y = - \frac{4}{7} x + 4 \text{ is the equation}$

thus slope $= - \frac{4}{7} \text{ and y-intercept} = 4$