Section 2.3 Notes: Rate of Change and Slope

Rate of change is a ratio that compares how much one quantity

changes, on average, relative to the change in another quantity. If

x is the independent variable and y is the dependent variable, then

the rate of change = This is sometimes referred to as change in

.change in

y

x.y

x

Example 1: 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 2: Find the rate of change for the data in the table.

Many real-world situations involve rates of change that are not constant, like the ones we’ve seen up to this point. These situations are often described as using an average rate of change over a specified interval. Example 3: 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 4: Refer to the graph. Find the average rate of change of the percent of households with computers in the United States from 2000 to 2004.

The slope of a line is the ratio of the change in the y-coordinates to the corresponding change in the x-coordinates. The slope of a line is the same as its rate of change.     

Example 5:  a) Find the slope of the line that passes through (–1, 4) and (1, –2).        b) Find the slope of the line that passes through (9, –3) and (2, 7).

Example 5 continued:   c) Find the slope of the line shown at the right.         d) Find the slope of the line shown at the right.