Chapter 7.4, Problem 8E

Solution

To Graph: The given inequality by using the hand sketch and state the boundary region.

  $y\ge -3$

The boundary $y=-3$ is included in the graph, and the graph of the inequality is shown as below,

  

Given Information:

The inequality is defined as,

  $y\ge -3$

Explanation:

Consider the given inequality,

  $y\ge -3$

Replacing the inequality symbol with the = symbol, the equation for the boundary is  $y=-3$ , which is a horizontal line.

The boundary point is included if the inequality containing $\le \text{ or }\ge$ symbols and the boundary point is excluded if the symbols $<\text{ or }>$  is used.

As the greater than equal to symbol was used, then the boundary is included in the graph and drawing it by using solid line.

To determine the half-plane to be shaded, use a test point not on the boundary, say  $\left(0,0\right)$ . Since,

  $0\ge -3$

The statement is true so shade the half-plane where  $\left(0,0\right)$

 is located. The graph will be:

  

Hence, the required graph is shown above and the boundary $y=-3$ is included in the graph.