Objectives: Find rates of change and slopes.

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Presentation transcript:

Objectives: Find rates of change and slopes. Relate a constant rate of change to the slope of a line.

“Rate of Change” is a fancy phrase for SLOPE in a real world problem. A rate of change is a ratio (fraction) that compares the change in a dependent variable (y) to the change in an independent variable (x). y x “Rate of Change” is a fancy phrase for SLOPE in a real world problem.

(Anywhere on this line the slope is the same!) Real world: Calculate the slope for ALL sections of the graph. 1 line – 1 slope (Anywhere on this line the slope is the same!)

1) The table shows the average temperature (°F) for five months in Columbia, TN. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? x y Identify the dependent and independent variables independent: month dependent: temperature

x y 2 to 3 3 to 5 5 to 7 7 to 8

During which time period did the temperature increase at the fastest rate? During which time period did the temperature increase at the greatest rate? The temperature increased at the greatest rate from month 5 to month 7.

Check It Out! Example 2 The table shows the balance of a bank account on different days of the month. Find the rate of change during each time interval. During which time interval did the balance decrease at the greatest rate? x y Step 1 Identify the dependent and independent variables. dependent: balance independent: day

x y Step 2 Find the rates of change. 1 to 6 6 to 16 16 to 22 22 to 30

During which time period did the balance decrease the fastest? During which time period did the temperature increase at the fastest rate? During which time period did the balance decrease the fastest? The balance declined at the greatest rate from day 1 to day 6.

3) The table shows the cost of using a computer at an Internet Café for a given amount of time. Find the rate of change in cost with respect to time. Time (hours) 2 4 6 Cost (dollars) 7 14 21

4) The table shows the cost to paint a house for a given number of hours. Find the rate of change in cost with respect to time. Time (hours) 4 6 8 Cost (dollars) 90 135 180

Correct on Guided Notes x y 2 -4 4 -1 5 8 10 3 13 7 Use the table to answer the following questions. 5) What is the rate of change between x = 5 and x = 8. 6) What is the rate of change between x = 2 and x = 10 7) Between what interval is the rate of change negative?