how to find rate of change on a graph

USING GRAPHS TO FIND RATES OF CHANGE

A rate of change is a ratio of the amount of change in the dependent variable to the amount of change in the independent variable.

In this section, we are going to see, how to use a graph to find rates of change.

Example 1 :

The graph shows the distance Nathan bicycled over time. What is Nathan's rate of change ?

Solution :

Step 1 :

Identify the independent and dependent variables.

Independent : Time

Dependent : Distance

Step 2 :

Find the rates of change.

0 hour to 1 hour :

Change in distance / Change in time = (15 - 0) / (1 - 0)

Change in distance / Change in time = 15 / 1

Change in distance / Change in time = 15

1 hours to 4 hours :

Change in distance / Change in time = (60 - 15) / (4 - 1)

Change in distance / Change in time = 45 / 3

Change in distance / Change in time = 15

2 hours to 4 hours :

Change in distance / Change in time = (60 - 30) / (4 - 2)

Change in distance / Change in time = 30 / 2

Change in distance / Change in time = 15

Nathan's rate of change is 15 miles per hour.

Reflect :

1. Recall that the graph of a proportional relationship is a line throughthe origin. Explain whether the relationship between Nathan's time and distance is a proportional relationship.

Yes ; the graph is a line through the origin.

2. Does it matter what interval you use when you find the rate of change of a proportional relationship ? Explain.

No ; in a proportional relationship, the rate of change is constant.

Example 2 :

The graph shows the rate at which water is leaking from a tank. Find the rate at which the water is leaking from the tank per minute.

Solution :

Step 1 :

Identify the independent and dependent variables.

Independent : Time

Dependent : Leakage

Step 2 :

Find the rates of change.

0 hours to 4 hours :

Leakage / Change in time = (3 - 0) / (4 - 0)

Leakage / Change in time = 3 / 4

Leakage / Change in time = 0.75

4 hours to 8 hours :

Leakage / Change in time = (6 - 3) / (8 - 4)

Leakage / Change in time = 3 / 4

Leakage / Change in time = 0.75

1 hour to 8 hours :

Leakage / Change in time = (6 - 0) / (8 - 0)

Leakage / Change in time = 6 / 8

Leakage / Change in time = 3 / 4

Leakage / Change in time = 0.75

The water is leaking at the rate of 0.75 gallons per minute.

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