# How do you graph inequalities y < x/3?

Apr 2, 2015

It is very simple. We need to graph $y = \frac{x}{3}$ first, then make modifications on that graph.

We need $2$ points to graph a line.

When $x = 0$:

$y = \frac{0}{3} \to 0$

When $x = 1$:

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

Now plot $\left(0 , 0\right)$ and $\left(1 , \frac{1}{3}\right)$ on the coordinate plane.

Since $y$ is not equal to $\frac{x}{3}$, $y$ cannot be equal to $0$ and $\frac{1}{3}$. Thus, we need to draw a dashed line on the coordinate plane.

Now take a random point which is not on the line $y = \frac{x}{3}$. For example $\left(1 , 1\right)$

$y < \frac{x}{3}$

$1 < \frac{1}{3}$ is not correct.

So the part of the coordinate plane which has $\left(1 , 1\right)$ will not be shaded because that part is not satisfying the inequality. We need to shade the other part of the plane, which rests below our dashed line.

So the graph is:

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