CCSS Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Mathematical Practices 8 Look for and express regularity in repeated reasoning.

Then/Now You graphed linear relations. Find rate of change. Determine the slope of a line.

Vocabulary rate of change slope

Example 1 Constant Rate of Change COLLEGE ADMISSIONS In 2004, 56,878 students applied to UCLA. In 2006, 60,291 students applied. Find the rate of change in the number of students applying for admission from 2004 to 2006.

Example 1 Constant Rate of Change Answer:

Example 1 Constant Rate of Change Answer: The rate of change is This means that the number of students applying for admission increased by each year.

Example 1 Find the rate of change for the data in the table. A.2 ft/min B.3 ft/min C.4 ft/min D.6 ft/min

Example 1 Find the rate of change for the data in the table. A.2 ft/min B.3 ft/min C.4 ft/min D.6 ft/min

Example 2 Average Rate of Change BUSINESS Refer to the graph below, which shows data on the fastest-growing restaurant chain in the U.S. during the time period of the graph. Find the rate of change of the number of stores from 2001 to 2006.

Example 2 Average Rate of Change Answer:

Example 2 Average Rate of Change Answer: Between 2000 and 2006, the number of stores in the U.S. increased at an average rate of 5.4(1000) or 5400 stores per year.

Concept

Example 3 Find Slope Using Coordinates Find the slope of the line that passes through (–1, 4) and (1, –2). Slope Formula (x 1, y 1 ) = (–1, 4), (x 2, y 2 ) = (1, –2) Simplify. Answer:

Example 3 Find Slope Using Coordinates Find the slope of the line that passes through (–1, 4) and (1, –2). Slope Formula (x 1, y 1 ) = (–1, 4), (x 2, y 2 ) = (1, –2) Simplify. Answer: –3

Example 3 Find the slope of the line that passes through (9, –3) and (2, 7). A. B. C. D.

Example 3 Find the slope of the line that passes through (9, –3) and (2, 7). A. B. C. D.

Example 4 Find Slope Using a Graph Find the slope of the line shown at the right. Slope Formula (x 1, y 1 ) = (–1, 0), (x 2, y 2 ) = (1, 1) Simplify. Answer:

Example 4 Find Slope Using a Graph Find the slope of the line shown at the right. Slope Formula (x 1, y 1 ) = (–1, 0), (x 2, y 2 ) = (1, 1) Simplify. Answer:

Example 4 Find the slope of the line. A. B. C. D.

Example 4 Find the slope of the line. A. B. C. D.