Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through the Explorations 1 through 3 on page 251. You will use what you know about inequalities. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 251)

1. y = x – 3
2. all ordered pairs below the graph of y = x – 3
3. y < x – 3; <; Sample answer: The point (4, 0) is in the shaded region, and to make the inequality true for that point the < symbol is needed.

Exploration 2 (page 251)

1. 0 ≥ –3

Exploration 3 (page 251)

1. 

   Sample answer: Graph y = x + 5 with a dashed line. Test the point (0, 0), which does not make the inequality true. Shade the half-plane that does not contain the point (0, 0).

2. 

   Sample answer: Graph y = + 1 with a solid line. Test the point (0, 0), which does make the inequality true. Shade the half-plane that contains the point (0, 0).

3. 

   Sample answer: Graph y = –x – 5 with a solid line. Test the point (0, 0), which does make the inequality true. Shade the half-plane that contains the point (0, 0).

Section 5-6 Lesson (pages 252-255)

This lesson presents how to graph a linear inequality in the coordinate plane so that in the next lesson you can graph systems of linear inequalities. You have graphed inequalities on a number line. Relate the solid and dashed lines in the coordinate plane to the closed and open circles used when inequalities in one variable are graphed on a number line. The closed and open circles are boundaries, creating two half-lines. The solid and dashed lines are boundaries, creating two half-planes.

Study and read Examples 1 through 6 carefully. You will want to use your graphing calculator. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 252-255)

1. No
2. No
3. Yes
4. Yes
5. 
   
   
6. 
   
   
7. 
   
   
8. 

9. y > x + 3

10. x + y > 19

11. y ≤ + 4
    
    Sample answer: (3, 0), You can buy 3 pounds of red peppers and no tomatoes; (1, 1), You can buy 1 pound of red peppers and 1 pound of tomatoes.