# How do you graph x - 3y < 6?

May 22, 2015

Consider the related equation
$x - 3 y = 6$

The x and y intercepts are easily calculated
$\left(0 , - 2\right) \text{ and } \left(6 , 0\right)$
Using these points it is simple to draw the corresponding line.
Note that the points on the line are not part of the given inequality
$x - 3 y < 6$, so you may want to draw this line using dashes.

You will need to shade one of the sides to indicate that it is the required solution set. If you are unsure which side to shade, consider the point $\left(x , y\right) = \left(0 , 0\right)$. Obviously $\left(0\right) - 3 \left(0\right) < 6$ so the point $\left(0 , 0\right)$ must be on the shaded (solution) side.

graph{x-3y<6 [-10, 10, -5, 5]}