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

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

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 2,331,542 - 1,850,093 Rate of Change = = = x x2 - x1 1910 - 1900 481,449 Rate of Change = 48,145 people/year 10

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 2,284,103 - 2,331,542 Rate of Change = = = x x2 - x1 1920 - 1910 -47,439 -4,744 people/year Rate of Change = 10 Note: Rate of change can be negative!

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 40 - 40 0 ft Rate of Change = = = = 0 ft/yr x2 - x1 1994 - 1993 1 yr 2) From 1994 to 1996. y2 - y1 42.5 - 40 2.5 ft Rate of Change = = = = 1.25 ft/yr x2 - x1 1996 - 1994 2 yrs 3) From 1996 to 1999. y2 - y1 -1.5 ft 41 - 42.5 Rate of Change = = = = -0.5 ft/yr x2 - x1 1999 - 1996 3 yrs