1. Holt Algebra 1 5-3 Rate of Change and Slope Evaluate the functions for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

2. Holt Algebra 1 5-3 Rate of Change and Slope Find rates of change and slopes. Relate a constant rate of change to the slope of a line. Objectives

3. Holt Algebra 1 5-3 Rate of Change and Slope A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

4. Holt Algebra 1 5-3 Rate of Change and Slope The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? dependent: temperature independent: month

5. Holt Algebra 1 5-3 Rate of Change and Slope The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? dependent: temperature independent: month

6. Holt Algebra 1 5-3 Rate of Change and Slope The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? dependent: temperature independent: month

7. Holt Algebra 1 5-3 Rate of Change and Slope The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? dependent: temperature independent: month

8. Holt Algebra 1 5-3 Rate of Change and Slope The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

9. Holt Algebra 1 5-3 Rate of Change and Slope Graph the data from Example 1 and show the rates of change.

10. Holt Algebra 1 5-3 Rate of Change and Slope If all of the connected segments have the same rate of change, then they all have the same steepness and together form a straight line. The constant rate of change of a line is called the slope of the line.

11. Holt Algebra 1 5-3 Rate of Change and Slope Find the slope of the line. (3, 2) (–6, 5)

12. Holt Algebra 1 5-3 Rate of Change and Slope Find the slope of the line that contains (0, –3) and (5, –5).

13. Holt Algebra 1 5-3 Rate of Change and Slope Find the slope of each line. A.B. C. D.

14. Holt Algebra 1 5-3 Rate of Change and Slope As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.

15. Holt Algebra 1 5-3 Rate of Change and Slope Tell whether the slope of each line is positive, negative, zero or undefined. A. B. C. D.

16. Holt Algebra 1 5-3 Rate of Change and Slope HW pp. 314-317/13-31 Odd, 34-41