1. 3-3 Slope as Rate of Change
Goal:
Interpret slope as rate of change in real life situations.
Eligible Content:
A / A / A / A

2. Vocabulary
Rate of Change – comparing two different quantities that are changing.
Rate of Change = change in one quantity change in other quantity

3. How to Find Rate of Change
Create ordered pairs from the given information (x, y)
Remember x is independent, y is dependent
Time is always independent
Find the slope between the two ordered pairs
Label your answer with two units
Example: miles per hour

4. Example #1
DRIVING TIME Use the table to find the rate of change. Explain the meaning of the rate of change.
38 miles per hour

5. Example #2
CELL PHONE The table shows how the cost changes with the number of minutes used. Use the table to find the rate of change. Explain the meaning of the rate of change.
$0.05 per minute

6. Example #3
TRAVEL The graph shows the number of U.S. passports issued in 2002, 2004, and Find the rate of change for 2002–2004. :
950,000 passports per year

7. Example #4
Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rate of change for 1995–2000. :
180,000 departures per year

8. Example #5
You are parachuting. At time t = 0 seconds, you open your parachute at h = 2500 feet above the ground. At t = 35 seconds, you are at h = 2115 feet. x y
2700
2500
2300
2100
1900
Height (feet)
Time (seconds)
What is your rate of change in height?
(0, 2500)
-11 feet per second.
The negative shows that you are falling.
(35, 2115)

9. Examples
You are traveling by car and leave home at 8:00 AM. At 11:00 you are 171 miles from home. Find the average rate of change in miles per hour.
You are typing a paper. At 5:15 PM you have typed 275 words. At 5:27 PM you have typed 660 words. Find the average rate of change in words per minute.
At Memorial Hospital there were 500 births in In 2010, there were 352 births. Find the average rate of change in number of births per year.
57 miles per hour
32 words per minute
-37 births per year

10. Practice
Worksheet – “3-3 Slope as Rate of Change”

11. Constant Rate of Change
Determine whether the function is linear. Explain.
Answer: The rate of change is constant. Thus, the function is linear.

12. Constant Rate of Change
Determine whether the function is linear. Explain.
Answer: The rate of change is not constant. Thus, the function is not linear.

13. Determine whether the function is linear. Explain.
A. Yes, the rate of change is constant.
B. No, the rate of change is constant.
C. Yes, the rate of change is not constant.
D. No, the rate of change is not constant.

14. Determine whether the function is linear. Explain.
A. Yes, the rate of change is constant.
B. No, the rate of change is constant.
C. Yes, the rate of change is not constant.
D. No, the rate of change is not constant.

15. Homework
Pages #14-18
#42