4.4 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 / A1.2.2.1.43-3 Slope as Rate of ChangeVocabularyRate of Change comparing two different quantities that are changing.

Rate of Change =

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

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.

Example #2$0.05 per minuteExample #3TRAVEL The graph shows the number of U.S. passports issued in 2002, 2004, and 2006. Find the rates of change for 20022004 and 20042006.

2002-2004: 950,000 passports per year

2004-2006:1,600,000 passports per yearExample #4Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 19952000 and 20002005.

1995-2000:180,000 departures per year

2000-2005:180,000 departures per year

xy 5 15 25 35 452700

2500

2300

2100

1900Height (feet)Time (seconds)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. What is your rate of change in height?(0, 2500)(35, 2115)Example #5-11 feet per second.The negative shows that you are falling.ExamplesYou 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 hour32 words per minute-37 births per yearPracticeWorksheet 3-3 Slope as Rate of Change

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

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

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.

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.

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