We have to manipulate the equation in order to make it easy to graph:
[tex]\begin{gathered} x-3y=6 \\ -3y=6-x \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]
We now know that the y-intercept is -2.
We also know that y increases by one unit when x increases by 3 units, by the meaning of the slope. We can verify that y=0 when x=6.
Then, with this information (we know 2 points of the line) we can graph:
