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4. Contents Lesson 8-5Rate of Change

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6. Lesson 5 Contents Example 1Find a Rate of Change Example 2Compare Rates of Change Example 3Write a Direct Variation Equation Example 4Use Direct Variation to Solve Problems

7. Example 5-1a School The graph shows Jadon’s quiz scores for the first five weeks after he joined a study group. Find the rate of change from Week 2 to Week 5. Definition of slope Simplify.

8. Example 5-1a Answer:The expected rate of change in quiz scores is an increase of about 4.3 points per week.

9. Example 5-1b Summer Camp The graph shows the number of campers enrolled at a summer camp during its first five years of operation. Find the rate of change from Year 2 to Year 5. Answer: an increase of about 71.7 campers per year

10. Income ($) YearMillersJoneses 200149, 00050, 000 200251, 00052, 000 200352, 50054, 500 200455, 00057, 000 Example 5-2a Income The table shows the yearly incomes of two families. Compare the rates of change. Millers rate of change

11. Example 5-2a Joneses rate of change Answer:The income of the Joneses increases at a faster rate than the income of the Millers.

12. Example 5-2b Income The table shows the yearly incomes of two families. Compare the rates of change. Income ($) YearBrownsGreens 199845, 00043, 000 199948, 50046, 000 200051, 00049, 500 200155, 00054, 000 Answer:The income of the Green family increases at a faster rate than the Brown family.

13. Example 5-3a Suppose y varies directly with x and when. Write an equation relating x and y. Step 1Find the value of k. Direct variation Replace y with 6 and x with 54. Simplify. Step 2Use k to write an equation. Direct variation Replace k with.

14. Example 5-3a Answer:A direct variation equation that relates x and y is.

15. Suppose y varies directly with x and when. Write an equation relating x and y. Example 5-3b Answer:

16. Example 5-4a Landscaping The depth of a wide hole for a backyard pond as it is being dug is recorded in the table. Write an equation that relates time and hole depth. Time (min) Hole Depth (in.) xy 108 2015 3024 4031

17. Example 5-4a Step 1 Find the ratio of y to x for each recorded time. These are shown in the third column of the table. The ratios are approximately equal to 0.8. 0.7753140 0.82430 0.751520 0.8 810 yx Answer: A direct variation equation that relates the time x and the hole depth y is. Step 2 Write an equation. Direct variation Replace k with 0.8.

18. Example 5-4a Predict how long it will take to dig a depth of 36 inches. Write the direct variation equation. Replace y with 36. Divide each side by 0.8. Answer: It will take about 45 minutes to dig to a depth of 36 inches.

19. Example 5-4b Assembly Line The number of units produced on a factory assembly line is recorded in the table. Time (min) x Units produced y 5 35 10 68 15105 20140 a. Write an equation that relates time and units produced. b. Predict how long it will take to produce 315 units. Answer: Answer: 45 minutes

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21. Pre-Alg.com Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Pre-Algebra 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.pre-alg.com/extra_examples.

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