###### Example4.10.8

Graph $$y\gt2x+1\text{.}$$

There are two steps to graphing this linear inequality in two variables.

1. Graph the line $$y=2x+1\text{.}$$ Because the inequality symbol is $$\gt$$ (instead of $$\ge$$), the line should be dashed (instead of solid).
2. Next, we need to decide whether to shade the region above $$y=2x+1$$ or below it. We will choose a point to test whether $$y\gt2x+1$$ is true. As long as the line doesn't cross $$(0,0)\text{,}$$ we will use $$(0,0)$$ to test because the number $$0$$ is the easiest number for calculation. \begin{align*} y\amp\gt2x+1\\ 0\amp\stackrel{?}{\gt}2(0)+1\\ 0\amp\stackrel{no}{\gt}1 \end{align*} Because $$0\gt1$$ is not true, the point $$(0,0)$$ is not a solution and should not be shaded. As a result, we shade the region without $$(0,0)\text{.}$$
in-context