1. Objective- To calculate the rate of change
between two points. x y
Karen’s age
Karen’s height 9
4’ 3’’ x y 11
4’ 9’’ y
4’9’’ - 4’3’’
Change in height
Rate of Change = = = x
11 - 9
Change in age y
4’9’’ - 4’3’’
6’’ = = =
3’’/ yr x
11 - 9
2 yrs

2. Formula for Rate of Change
Given two points (x1 , y1 ) and (x2 , y2 )... y
y2 - y1
Rate of Change = = x
x2 - x1

3. Look at the graph on page 417 in your textbook.
a) Find the rate of change in population between
1900 and 1910.
year
population
1900
1,850,093 x y
1910
2,331,542 y
y2 - y1
2,331, ,850,093
Rate of Change = = = x
x2 - x1
481,449
Rate of Change =
48,145 people/year 10

4. Look at the graph on page 417 in your textbook.
b) Find the rate of change in population between
1910 and 1920.
year
population
1910
2,331,542 x y
1920
2,284,103 y
y2 - y1
2,284, ,331,542
Rate of Change = = = x
x2 - x1
-47,439
-4,744 people/year
Rate of Change = 10
Note: Rate of change can be negative!

5. Find the indicated rate of change.
year
Oak tree height
1993
40 ft.
1994
40 ft.
1996
42.5 ft.
1999
41 ft.
1) From 1993 to 1994.
y2 - y1
0 ft
Rate of Change = = = =
0 ft/yr
x2 - x1
1 yr
2) From 1994 to 1996.
y2 - y1
2.5 ft
Rate of Change = = = =
1.25 ft/yr
x2 - x1
2 yrs
3) From 1996 to 1999.
y2 - y1
-1.5 ft
Rate of Change = = = =
-0.5 ft/yr
x2 - x1
3 yrs