# How do you find the slope and intercept of 5 - 1/3y = 2x?

Aug 28, 2016

slope = - 6 , y-intercept = +15

#### 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 $5 - \frac{1}{3} y = 2 x \text{ in this form}$

subtract 5 from both sides.

$\Rightarrow \cancel{5} - \cancel{5} - \frac{1}{3} y = 2 x - 5 \Rightarrow - \frac{1}{3} y = 2 x - 5$

multiply through by - 1 : $\frac{1}{3} y = - 2 x + 5$

now multiply both sides by 3.

$\Rightarrow {\cancel{3}}^{1} \times \frac{1}{\cancel{3}} ^ 1 y = - 6 x + 15 \Rightarrow y = - 6 x + 15$

The equation is now in the form $\textcolor{b l u e}{y = m x + b}$

$\Rightarrow \text{slope" =-6" and y-intercept} = + 15$
graph{-6x+15 [-45.63, 45.6, -22.74, 22.9]}