Question

Graph each inequality.$\mathit{y}\mathbf{<}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{1}$

Short answer

A graph of given inequality is

Step-by-step solution

Step 1. Write steps to graph inequality.

1. If an inequality contains $<\text{or}>$, then use dotted line and if an inequality contains $\le \text{or}\ge$, then use solid line.

2. Use test point to determine which half plane should be shaded.

3. Shade the half plane that contains the solution.

Step 2. Select a test point.

Let $(0,0)$be a test point. Substitute 0 for $x$and 0 for $y$into $y<2x+1$.

role="math" localid="1647505236606" $\begin{array}{c}0<2\left(0\right)+1\\ 0<1\end{array}$

Therefore, the half plane containing the origin is the solution.

Step 3. Graph an inequality.

Graph an inequality, $y<2x+1$and shade the half plane containing test point.