Chapter 10.9, Problem 4E

To determine

To graph: the given inequality.

Answer to Problem 4E

  

Explanation of Solution

Given:

  $y\ge -2$

Calculation:

Consider the inequality

  $y\ge -2$

Graph the inequality $y\ge -2$ .

To graph the inequality $y\ge -2$ simply graph the boundary line $y=-2$ , which is a horizontal line.

Clearly, the points on the line itself satisfy the inequality because, the inequality contains $\ge$ symbol, so, graph the boundary line with a solid curve.

To determine whether the above or below region of the horizontal line satisfies the inequality, use the test points $\left(2,-3\right)$ on the below side and (1, 2) on the above side of the line.

Substitute the coordinates of each point in the inequality and check whether the result satisfies the inequality.

The computations are tabulated as shown below:

Test Point			Conclusion
$\left(2,-3\right)$	$-3\cancel{\ge }-2$		Part of the graph
$\left(1,2\right)$	$2\ge -2$		Not a part of the graph

From the above table, observe that the points above the line are satisfies the inequality.

So, shade the region above the horizontal line on the graph.

The graph of the inequality $y\ge -2$ is shown below:

  

Conclusion:

Therefore, the graph of inequality is drawn.