3-3 Slope as Rate of Change Goal: Interpret slope as rate of change in real life situations. Eligible Content: A1.2.1.1.1 / A1.2.2.1.1 / A1.2.2.1.2 / A1.2.2.1.4

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

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

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

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

Example #3 TRAVEL The graph shows the number of U.S. passports issued in 2002, 2004, and 2006. Find the rates of change for 2002–2004 and 2004–2006. 2002-2004: 950,000 passports per year 2004-2006: 1,600,000 passports per year

Example #4 Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 1995–2000 and 2000–2005. 1995-2000: 180,000 departures per year 2000-2005:

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 5 15 25 35 45 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)

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 2006. 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

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

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

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.

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.

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.

Homework Pages 177-179 #14-18 #20-23 #42