Chapter 1.8, Problem 3CFU

To determine

To explain: the use of test point to determine the region(s) of the graph of an inequality to be shaded.

Answer to Problem 3CFU

Since inequality represents a region where the line is the boundary, or the edge, so true test point allows you to shade the region of the inequality.

Explanation of Solution

Given information:

Test points are used for shading the region in the graph.

Calculation:

Let’s take an inequality representing the dotted line $y>x+1$ . The dotted line will divide the coordinate plane in half as shown below.

  

Now put point coordinates on the graph in each region as shown below.

  

Put the point coordinate in the inequality and find the test point (i.e. true and false points) as shown below.

  $\begin{array}{l}\text{Point in top region }\left(1,3\right)\\ y>x+1\\ 3>1+1\\ 3>2\end{array}$

This test point is true.

  $\begin{array}{l}\text{Point in bottom region }\left(0,0\right)\\ y>x+1\\ 0>0+1\\ 0>1\end{array}$

This test point is false.

The region showing having the true test point will be shaded.

  

Since inequality represents a region where the line is the boundary, or the edge, so true test point allows you to shade the region of the inequality.