Chapter 5.6, Problem 20E

To determine

To graph the inequality

  $y>6$

Answer to Problem 20E

  

Explanation of Solution

Given:

  $y>6$

Concept Used:

To graph an inequality $y\le a\text{ or }y<a$ , follow the steps:

1. First graph the line , $y=a$ use a solid line if the inequality is not strict $\left(\le \text{ or }\ge \right)$ , and use a dotted line in the inequality is strict $\left(<\text{ or }>\right)$ .
2. Test if ordered point $\left(0,0\right)$ satisfies the inequality.
3. If $\left(0,0\right)$ is a solution, shade the half plane that contains $\left(0,0\right)$ , else shade other half plane that does not contain $\left(0,0\right)$ .

Calculation:

In order to graph the inequality

  $y>6$

First graph the line $y=6$ and since the inequality is strict, thus use dotted line to draw it.

Now, check if the ordered point $\left(0,0\right)$ satisfies the given inequality, for that substitute x and y as 0. As,

  $0>6$

But, $0\cancel{>}6$ . Thus, $\left(0,0\right)$ does not satisfy the given inequality, thus the area to be shaded will be the half plane that does not contain $\left(0,0\right)$ .

From the above calculation, graph of the inequality $y>6$ is represented by using a graphing utility, as: