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A rate of change compares the change in one
quantity relative to a change in another
quantity
Unlike slope, a rate of change is expressed in
units (Example:
km/h)
Thus, speed is
one example of
a rate of change.
Time (s)
Ave
rag
e D
ista
nce
(m
)
20 4 6 8 10 12 14 16 18 20
50
100
150
200
250
300
Cheetah (10,311)
Professional Cyclist (10,165)
Polar Bear (10,111)
Olympic Sprinter (10,102)
Average Running Distance vs. Time
This graph shows the average distance, in meters, that each
animal or person can run in 10s.
Example
Time (s)
Ave
rag
e D
ista
nce
(m
)
20 4 6 8 10 12 14 16 18 20
50
100
150
200
250
300
Cheetah (10,311)
Professional Cyclist (10,165)
Polar Bear (10,111)
Olympic Sprinter (10,102)
Average Running Distance vs. TimeVisually compare the
steepness of each graph, then determine
the slope. Rank the slopes from greatest
to least.
Solutions:
m (Cheetah) = 311/10 = 31.1
m (Cyclist) = 165/10 = 16.5
m (Bear) = 111/10 = 11.1
m (Sprinter) = 102/10 = 10.2
Time (s)
Ave
rag
e D
ista
nce
(m
)
20 4 6 8 10 12 14 16 18 20
50
100
150
200
250
300
Cheetah (10,311)
Professional Cyclist (10,165)
Polar Bear (10,111)
Olympic Sprinter (10,102)
Average Running Distance vs. Time
How do we find the speed of an object, animal, or person?
Solutions:
m (Cheetah) = 311/10 = 31.1
m (Cyclist) = 165/10 = 16.5
m (Bear) = 111/10 = 11.1
m (Sprinter) = 102/10 = 10.2
Speed = distance time
Calculate the speed
of each person or
animal
Time (s)
Ave
rag
e D
ista
nce
(m
)
20 4 6 8 10 12 14 16 18 20
50
100
150
200
250
300
Cheetah (10,311)
Professional Cyclist (10,165)
Polar Bear (10,111)
Olympic Sprinter (10,102)
Average Running Distance vs. TimeWhat do you
notice about the slope compared to the speed of each person or animal?
They are the SAME!
Thus, the rate of change between two variables is
equal to the slope of the line when the two variables are
graphed.
A rate of change is typically calculated as:
Rate of Change = change in dependent variable change in independent variable
Subtract the two
dependent variables
Subtract the two
independent variables
Slope = change in y change in x
Slope =
12
12
xx
yy
Practice (homework):
p. 268 #2, 3, 5, 7, 12, 14
