INTERPRETING LINE GRAPHS

By observing the upward or downward slant of the lines connecting the points, you can describe the trends in the data and predict future events.

Example 1 :

The temperature of water in a kettle is graphed over a 10 minute period.

a)  What was the room temperature when the kettle was switched on ?

b)  How long did it take for the water to boil ?

c)  For how long did the water boil ?

d)  At what times was the water temperature 50^oC ?

e)  During what period was the temperature decreasing ?

Solution :

(a)  At that time when kettle was switched on, the time will be 0. 

By observing the graph the value on the vertical axis at 0 is 20.

(b)  Boiling temperature of water is 100^o C, to reach boiling temperature is 2 minutes.

(c)  The water is boiling 1 minute.

(d)  At 7.5  minutes the temperature of water will be at 50^o C .

(e)  After 3 minutes the temperature is being decreased.

Example 2 :

Managers of a retail store conduct a customer count to help them decide how to roster their sales staff. The results are shown in the line graph.

a)  At what time was the number of people in the store greatest ?

b)  At what time was the number of people in the store least?

c)  Describe what happened in the store between 3 pm and 4 pm.

d)  Use the graph to estimate the number of people in the store at 9:30 am. 

Solution :

(a)  At 11 am the number of people in the store greatest.

(b)  At 8 pm the number of people will be less.

(c)  Between 3 pm to 4 pm, the number of customers being increased.

(d)  At the time 9.30 am, approximately 45 people will be there.

Example 3 :

When a bottle of soft drink was placed in a refrigerator, its temperature was measured at 5-minute intervals. The results are graphed alongside. 

a)  Determine the temperature of the liquid when it was first placed in the refrigerator.

b)  Find the time taken for the temperature to drop to 20^o C.

c)  Find the temperature after 10 minutes in the refrigerator.

d)  Find the fall in temperature during

(i)  the first 15 minutes (ii)  the next 15 minutes.

Solution :

(a)  The temperature of liquid when it was first placed in the refrigerator is 40^o C.

(b)  To drop the temperature 20^o C, it will take 15 minutes.

(c)  The temperature after 10 minutes is 25^o C.

(d)  In first 15 minutes, the temperature dropped 18^o C, and in the next 15 minutes the temperature has dropped 7^o C

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