**Finding rate of change from a graph worksheet :**

Worksheet on finding rate of change from a graph is much useful to the students who would like to practice problems on calculating rates of change using graphs.

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

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.

**Question 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.

**Question 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.

After having gone through the stuff given above, we hope that the students would have understood, how to find rate of change from a graph

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