GRAPHING LINEAR INEQUALITIES in TWO VARIABLES with the TI Nspire

NAME: ______

GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES WITH THE TI NSpire

To graph the linear inequality y < - x + 3, we first graph the related boundary equation y = - x + 3. The resulting boundary line contains all ordered pairs that are solutions to the equation y = - x + 3. This line separates the plane into two half-planes. All points “above” the boundary line have coordinates that satisfy the inequality y > - x + 3, and all points “below” the line have coordinates that satisfy the inequality y < - x + 3.

Since the inequality sign is a < symbol, graph a dashed line indicating that points on the line are not solutions of the inequality.

Choose a test point not on the boundary line. (0,0)

y < - x + 3

0 < - 0 + 3

0 < 3True

Since a true statement is obtained, shade the half-plane that contains the test point. If a false statement had been obtained, you would have shaded the half-plane that did not contain the test point.

The graph, or solution region, for y < - x + 3, then, is the half-plane below the boundary line and is shown shaded in the graph. The boundary line is shown dashed since it is not a part of the solution region.

The following steps may be used to graph linear inequalities in two variables.

A.)Graph the boundary line found by replacing the inequality sign with an equal sign. If the inequality sign is < or >, graph a dashed line indicating that points on the line are not solutions of the inequality. If the inequality sign is ≤ or ≥, graph a solid line indicating that points on the line are solutions of the inequality.

B.)Choose a test point not on the boundary line and substitute the coordinates of this test point into the original inequality.

C.)If a true statement is obtained instep 2, shade the half-plane that contains the test point. If a false statement is obtained, shade the half-plane that does not contain the test point.

Let’s try this problem on the TI NSpire.

Press the Home Key

Choose 1: New Document

Press Enter

Select 2: Add Graphs

Press Enter

The graph screen appears, however, there is an equal sign and we want a less than symbol, <.

Press the Delete Key

The inequalities symbols automatically appear.

Choose 2: <

The equals sign disappears and the less than symbol is inserted where the equals sign had previously been located.

Type the inequality function into the NSpire.

Press Enter

Why is the line a dashed line? ______

Why is the region shaded below the dashed line? ______

2.)Graph y ≥ 2x + 4 on the graph paper and check it on the TI NSpire.

3.)Graph y -3x + 1 on the graph paper and check it on the TI NSpire.

4.)Graph y ≤ 4x - 9 on the graph paper and check it on the TI Nspire.

5.)Graph y ≤ x - 4 on the graph paper and check it on the TI Nspire.

6.)Graph y x + 7 on the graph paper and check it on the TI NSpire.