Chapter 5.6, Problem 43E

To determine

To find: whether $\left(0,0\right)$ use as test point when graphing an inequality.

Answer to Problem 43E

  $\left(0,0\right)$ cannot be taken as test pair when it is on the boundary line.

Explanation of Solution

Given:

Origin $\left(0,0\right)$ .

Concept used:

When the point is on the boundary line it cannot be test pair.

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

Calculation:

The objective is to find the if it can always use $\left(0,0\right)$ as the test pair when graphing the inequality.

  $x>y$ , let’s consider an inequality.

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

Step 2: graph the inequality.

  

As $\left(0,0\right)$ in on the line it wouldn’t tell which side of the graph need to be shaded.

Hence, $\left(0,0\right)$ cannot be taken as test pair when it Is on the boundary line.