Rate of Change MathScience Innovation Center Betsey Davis.

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


slope slant tilt incline grade hill rise angle

gradient lean run pitch rate of

change


4 types of slope(read left to right like sentence )

positive negative zero or no slope undefined


Which has the greatest slope?

x

y

bc

a

c


Find the slope of each

x

y

bc

a

a) m = .29

b) m = .56

c) m = 1.67


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


Now… tell the real world meaning of slope

time

distance

Speed !Speed !


Compare speeds between intervals

a

b

d

c

time

distance

fastest?slowest?

between a and b

stopped between b and c



time

speed

Acceleration!Acceleration!


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



minute

Total

Call

cost

cost per minutecost per minute

Cellular phone usage


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


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


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

Rate of Change MathScience Innovation Center Betsey Davis.

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