Chapter 5.6, Problem 41E

To determine

To find: the reason of choosing a test point that is not on the boundary line when graphing a linear inequality.

Answer to Problem 41E

The ordered pair on the boundary does not give the solution of the inequality. As it would not tell which side of the graph can be shaded. Only the pair on either side of the boundary line gives the solution of the inequality.

Explanation of Solution

Given:

Linear inequality.

Concept used:

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but the are of the coordinate plane that satisfy the inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

The objective is to find the reason why must it choose a test pair which is not on the boundary line.

  $x>y$ let us consider an inequality.

Step $1$ : graph $x=y$ . Use a dashed a line because the inequality symbol is $>$ .

Step 2: Graph the inequality.

If it takes the ordered pair on the boundary line $\left(-2,-2\right)$ . $-2$ is not greater than $-2$ . But it is equal to $-2$ . The ordered pair is not the solution, also it would not tell which side of the graph has to be shaded.

Hence, the ordered pair on the boundary does not give the solution of the inequality. As it would not tell which side of the graph can be shaded. Only the pair on either side of the boundary line gives the solution of the inequality.