Graphs of Linear Inequalities: example 4.73

First we graph the boundary line $x-2y=5$. The inequality is $<$ so we draw a dashed line.

Then we test a point. We’ll use $\left(0,0\right)$ again because it is easy to evaluate and it is not on the boundary line.

Is $\left(0,0\right)$ a solution of $x-2y<5$?

The point $\left(0,0\right)$ is a solution of $x-2y<5$, so we shade in that side of the boundary line.