5 3 Rate of Change and Slope Holt

5 -3 Rate of Change and Slope Holt Algebra 1 HONORS

Objectives: 1. Find rates of change and slopes. 2. Relate a constant rate of change to the slope of a line.

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.

5 -3 Rate of Change and Slope Holt Algebra 1

5 -3 Rate of Change and Slope Real world: Calculate the slope for ALL sections of the graph. Holt Algebra 1 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

5 -3 Rate of Change and Slope During which time period did the temperature increase at the greatest rate? temperature increased at theincrease greatest ratefastest rate? During. The which time period did the temperature at the from month 5 to month 7. Holt Algebra 1

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 Identify the dependent and independent variables. independent: day dependent: balance

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

5 -3 Rate of Change and Slope During which time period did the balance decrease the fastest? The balance declined at the greatest rate from day 1 to day 6. During which time period did the temperature increase at the fastest rate? Holt Algebra 1

5 -3 Rate of Change and Slope 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 Holt Algebra 1

5 -3 Rate of Change and Slope 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 Holt Algebra 1

5 -3 Rate of Change and Slope 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? Holt Algebra 1 x y 2 -4 4 -1 5 0 8 5 10 3 13 7

5 -3 • Rate of Change and Slope Holt Algebra 1