# How do you find the slope of x-3y= -3?

Aug 21, 2015

$m = \frac{1}{3}$

#### Explanation:

You can find the slope of this line by rearranging the equation to math slope-intercept form, which for a general form line looks like this

$\textcolor{b l u e}{y = m x + b}$

$x - 3 y = - 3$

Start by moving $x$ to the right-hand side of the equation

$- 3 y = - x - 3$

Now divide both sides of the equation by $- 3$ to get $y$ alone on the left-hand side

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(- 3\right)}}} \cdot y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(- 3\right)}}}} = \frac{\left(- 1\right)}{\left(- 3\right)} x + \frac{\left(- 3\right)}{\left(- 3\right)}$

$y = \frac{1}{3} x + 1$

Compare this euqation to the general form slope-intercept form to get the value of the slope, which in your case is

$m = \textcolor{g r e e n}{\frac{1}{3}}$