Example4.11.15

Graph \(y\gt2x+1\text{.}\)

There are two steps to graph an inequality.

  1. Graph the line \(y=2x+1\text{.}\) Because the inequality symbol is \(\gt\text{,}\) (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{gather*} y\gt2x+1\\ 0\stackrel{?}{\gt}2(0)+1\\ 0\stackrel{?}{\gt}1 \end{gather*} 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 \((0,0)\text{.}\)
This is a coordinate plane with y=2x+1 graphed.
This is a coordinate plane with y=2x+1 graphed. The region above the line is shaded.
Figure4.11.16Step 1 of graphing \(y\gt2x+1\)
Figure4.11.17Step 2 of graphing \(y\gt2x+1\)
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