Topics
12. Data
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AustraliaNSW
Stage 3

12.05 Line graphs

Lesson
Practice
Lesson

Are you ready?

Do you recall how to plot points on the  coordinate plane  ?

Examples

Example 1

Plot the point (6,3) onto the number plane.

Worked Solution
Create a strategy

Use the numbers on the axes to move on the coordinate plane.

Apply the idea

Start at (0,\,0). Plot the point 6 spaces to the right, then 3 spaces up.

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Idea summary

The coordinate plane has an x-axis which runs horizontally and a y-axis which runs vertically.

Each coordinate pair has an x-coordinate and a y-coordinate.

Line graphs

This video explains all the important features of a line graph.

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Examples

Example 2

A dachshund puppy is weighed every two weeks.

Week2468
Weight (kg)1455
a

Construct a line graph of the information given in the table.

Worked Solution
Create a strategy

Plot the points from the table and join them with straight lines.

Apply the idea
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\text{Week}
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\text{Weight}

The number of weeks will go on the horizontal axis, and the weight will go on the vertical axis since it depends on the number of weeks.

The points from the table are (2, 1),\,(4,4),\,(6,5),\,(8,5). So we can plot these on the graph, then join them with straight lines.

b

How much weight had the puppy gained from week 2 to week 4?

Worked Solution
Create a strategy

To find the change in weight, subtract the weight in week 2 from the weight in week 4.

Apply the idea
\displaystyle \text{Weight gained}\displaystyle =\displaystyle 4-1Subtract the weights
\displaystyle =\displaystyle 3\, \text{kg}
c

In which weeks did the puppy's weight not change?

A
From week 4 to week 6.
B
From week 6 to week 8.
Worked Solution
Create a strategy

Look for the horizontal part in the line graph.

Apply the idea

If the puppy's weight did not change then the line graph will be horizontal. We can see a horizontal line from week 6 to week 8.

So the correct answer is option B.

Idea summary

Line graphs use connected points plotted in a number plane to show data.

Create and interpret line graphs

This video shows us how to create a line graph and all the things we should consider.

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Examples

Example 3

The price of chocolate bars over a year has been graphed below.

The image shows a line graph for the price of chocolate bars over a year. Ask your teacher for more information.
a

What was the lowest price of the chocolate bars?

Worked Solution
Create a strategy

Find the price on the vertical axis that has the lowest points.

Apply the idea

We can see from the graph that the lowest points match \$1.25 in the vertical axis.

The lowest price of the chocolate bars is \$1.25.

b

In which months was the price the lowest?

Worked Solution
Create a strategy

Find the months with the lowest points from part (a).

Apply the idea

We can see from the graph that the lowest points are at March and October.

March and October were the months the price was the lowest.

c

What was the highest price of the chocolate bars?

Worked Solution
Create a strategy

Find the price on the vertical axis that has the highest points.

Apply the idea

We can see from the graph that the highest points match \$2.50 in the vertical axis.

The highest price of the chocolate bars is \$2.50.

Idea summary

Line graphs are most useful when we want to track the change of something over time. Some things we could use a line graph for include:

  • rainfall over a period of time

  • the time the sun rises each day

  • the value of the Australian dollar compared to the US Dollar, over time

Outcomes

MA3-18SP

uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

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