2. Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

3. Splash Screen

4. Contents Lesson 5-1Slope

5. Lesson 1 Contents Example 1Positive Slope Example 2Negative Slope Example 3Zero Slope Example 4Undefined Slope Example 5Find Coordinates Given Slope Example 6Find a Rate of Change

6. Example 1-1a Find the slope of the line that passes through (–3, 2) and (5, 5). Let and Substitute.

7. Example 1-1b Simplify. Answer:The slope is

8. Example 1-1c Find the slope of the line that passes through (4, 5) and (7, 6). Answer:

9. Example 1-2a Find the slope of the line that passes through (–3, –4) and (–2, –8). Substitute. Let and

10. Example 1-2b Answer:The slope is –4. Simplify.

11. Example 1-2c Find the slope of the line that passes through (–3, –5) and (–2, –7). Answer: –2

12. Let and Example 1-3a Find the slope of the line that passes through (–3, 4) and (4, 4). Substitute.

13. Example 1-3b Answer:The slope is 0. Simplify.

14. Example 1-3c Find the slope of the line that passes through (–3, –1) and (5, –1). Answer: 0

15. Let and Example 1-4a Find the slope of the line that passes through (–2, –4) and (–2, 3). Answer:Since division by zero is undefined, the slope is undefined.

16. Example 1-4b Find the slope of the line that passes through (5, –1) and (5, –3). Answer:undefined

17. Example 1-5a Find the value of r so that the line through ( 6, 3 ) and ( r, 2 ) has a slope of Slope formula Substitute. Subtract.

18. Example 1-5b Find the cross products. Simplify. Add 6 to each side. Answer:Simplify.

19. Example 1-5c Find the value of p so that the line through ( p, 4 ) and ( 3, –1 ) has a slope of Answer: –5

20. Example 1-6a Travel The graph to the right shows the number of U.S. passports issued in 1991, 1995, and 1999. Find the rates of change for 1991-1995 and 1995-1999. Use the formula for slope. millions of passports years

21. Example 1-6b 1991-1995: Substitute. Simplify. Answer: The number of passports issued increased by 1.9 million in a 4-year period for a rate of change of 475,000 per year.

22. Example 1-6c 1995-1999: Substitute. Simplify. Answer: Over this 4-year period, the number of U.S. passports issued increased by 1.4 million for a rate of change of 350,000 per year.

23. Example 1-6d Explain the meaning of slope in each case. Answer: For 1991-1995, on average, 475,000 more passports were issued each year than the last. For 1995- 1999, on average, 350,000 more passports were issued each year than the last.

24. Example 1-6e How are the different rates of change shown on the graph? Answer: There is a greater rate of change from 1991- 1995 than from 1995-1999. Therefore, the section of the graph for 1991-1995 has a steeper slope.

25. Example 1-6f Airlines The graph shows the number of airplane departures in the United States in recent years. a.Find the rates of change for 1990-1995 and 1995-2000. Answer:240,000 per year; 180,000 per year

26. Example 1-6g b.Explain the meaning of the slope in each case. Answer:For 1990-1995, the number of airplane departures increased by about 240,000 flights each year. For 1995- 2000, the number of airplane departures increased by about 180,000 flights each year.

27. Example 1-6h c.How are the different rates of change shown on the graph? Answer:There is a greater vertical change for 1990-1995 than for 1995-2000. Therefore, the section of the graph for 1990-1995 has a steeper slope.

28. End of Lesson 1

29. Algebra1.com Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Algebra 1 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.algebra1.com/extra_examples.

30. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

31. Transparency 1a

32. End of Slide Show