###### Example4.10.11

Graph $$y\leq -\frac{5}{3}x+2\text{.}$$

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

1. Graph the line $$y= -\frac{5}{3}x+2\text{.}$$ Because the inequality symbol is $$\leq$$ (instead of $$\lt$$), the line should be solid.
2. Next, we need to decide whether to shade the region above $$y= -\frac{5}{3}x+2$$ or below it. We will choose a point to test whether $$y\leq -\frac{5}{3}x+2$$ is true there. Using $$(0,0)$$ as a test point:
\begin{align*} y\amp\leq -\frac{5}{3}x+2\\ 0\amp\stackrel{?}{\leq}-\frac{5}{3}(0)+2\\ 0\amp\stackrel{\checkmark}{\leq}2 \end{align*}
Because $$0\leq2$$ is true, the point $$(0,0)$$ is a solution. As a result, we shade the region with $$(0,0)\text{.}$$
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