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Rate of Change
MathScience Innovation CenterBetsey Davis
Rate of Change B. Davis MathScience Innovation Center
Slope symbol: m the change in y divided by the change in x y/ x how fast y changes compared to x the ratio of changes in y and x rate of growth of the dependent variable rate of change
Rate of Change B. Davis MathScience Innovation Center
slope slant tilt incline grade hill rise angle
gradient lean run pitch rate of
change
Rate of Change B. Davis MathScience Innovation Center
4 types of slope(read left to right like sentence )
positive negative zero or no slope undefined
Rate of Change B. Davis MathScience Innovation Center
Which has the greatest slope?
x
y
bc
a
c
Rate of Change B. Davis MathScience Innovation Center
Find the slope of each
x
y
bc
a
a) m = .29
b) m = .56
c) m = 1.67
Rate of Change B. Davis MathScience Innovation Center
Find the slope of the line connecting ( 1,4 ) and ( 5, 6) m = 2/4 or .5 connecting ( 10,1 ) and ( 5, 3) m = - 2/5 or - .4
Rate of Change B. Davis MathScience Innovation Center
Now… tell the real world meaning of slope
time
distance
Speed !Speed !
Rate of Change B. Davis MathScience Innovation Center
Compare speeds between intervals
a
b
d
c
time
distance
fastest?slowest?
between a and b
stopped between b and c
Rate of Change B. Davis MathScience Innovation Center
Now… tell the real world meaning of slope
time
speed
Acceleration!Acceleration!
Rate of Change B. Davis MathScience Innovation Center
Compare speeds between intervals
a
b
d
c
time
speed
fastest?slowest?
at dat a
What is happening between b and c?
steady speed,
0 acceleration
Rate of Change B. Davis MathScience Innovation Center
Now… tell the real world meaning of slope
minute
Total
Call
cost
cost per minutecost per minute
Cellular phone usage
Rate of Change B. Davis MathScience Innovation Center
Compare costs
a
b
d
c
minute
Total
Call
cost
most expensive rate?least ?
between a and bbetween b and c
What is happening between b and c?
steady cost, no increase in rate
Rate of Change B. Davis MathScience Innovation Center
Tell the real world meaning of slope at the movies
tickets sold
income
price of one ticketprice of one ticket
Movie Ticket Sales Office Report
Rate of Change B. Davis MathScience Innovation Center
Tell the real world meaning of slope
time
H2 O
remaining
in tub
how fast water drainshow fast water drains
Draining the bath tub after washing the dog