Rate of Change

Learning Goals

• I can calculate and interpret the rate of change from a graph and a table of values

• I can identify the units of rate of change given the units of the two variables

Rate of change

• What does the “rate of change” mean in the context of this situation?

• How could we find it?• What other names do we have for the “rate of change”?

How to calculate Rate of Change, AKA Slope

• Select the two points between which you want to know the rate of change. • It’s helpful to label one point as (x1, y1) and the other as (x2, y2)

• Complete the formula for slope:• y2-y1

x2-x1

• This formula means: change from one y to anotherchange from one x to another

Rate of ChangeEx. 1

• Calculate the rate of change

• What does the rate of change mean here?

Time (min)

Height of airplane (m)

0 20004 1400

Comparing Rate of Change Ex. 2

• The distance required to stop a car depends on the speed at which the car is travelling

• These tables show the reaction distance and braking distance needed to stop a car on dry pavement for given speeds• REACTION Distance: the distance the car travels from the

time the driver decides to stop the car until he/she applies the brakes

• BRAKING Distance: the distance the car travels from the time the brakes are applied until the car actually stops.

Comparing Rates of Change Ex. 2

SPEED (km/h)

REACTION Distance (m)

0 0

10 2

20 4

30 6

40 8

50 10

Change in distanceChange in speed Description of the

Rate of Change:

SPEED (km/h)

BRAKING Distance (m)

0 0.0

10 0.5

20 2.0

30 4.5

40 8.0

50 12.5

Change in distanceChange in speed Description of the

Rate of Change:

Comparing Rates of Change Ex. 2

Graph it!

• Describe how the graph reflects the rates of change across the data

Example 2

Identifying Rates of Change in a Table & Graph

• This table shows the change in height of a tomato plant from germination until the tomatoes ripen.

TIME (weeks)

0 2 4 6 8 10 12 14 16 18HEIGHT (cm)

0 5 10 20 40 58 75 86 90 90

• Determine when the rate of change in the height is:• i) Zero ii) Constant iii) Changing

• This table shows the change in height of a tomato plants from germination until the tomatoes ripen.TIME (weeks)

0 2 4 6 8 10 12 14 16 18

HEIGHT (cm)

0 5 10 20 40 58 75 86 90 90

• Determine when the rate of change in the height is:• i) Zero ii) Constant iii) Changing

• STEP 1: Find the first differences• STEP 2: Graph the data

Consolidate Rates of Change

• GIVEN A TABLE OR GRAPH, WE CAN IDENTIFY WHEN THE RATE OF CHANGE IS ZERO, CONSTANT, OR CHANGING WITHOUT ACTUALLY CALCULATING THE RATES OF CHANGE• In a table,

we look at the first differences

• In a graph, we decide whether the points lie on a line

Identifying Rates of Change in a Table or Graph

RATE OF CHANGE

TABLE Ex. of GRAPH

Zero

Constant

Changing

Learning Goals

• I can calculate and interpret the rate of change from a graph and a table of values• I can identify the units of rate of change

given the units of the two variables

Homework: Pg. 284 # 2-4, 7, 11