Graphs

A graph is a diagram of values which shows the relationship between given information or data.

Some of the graphs studied in Grade 6 include bar graphs, double bar graphs, pie charts and pictographs.

Examples

Example of a Bar Graph

Example of a Double Bar Graph

Example of a Pie Chart

Example of a Pictogram

In Grade 7 we are going to study two types of line graphs, i.e., linear and non-linear graphs.

Linear means in a straight line, so a linear graph is a graph that increases or decreases in a straight line.

Example of a Linear Graph

A non-linear graph is a graph that increases or decreases in a curved or broken line.

Example of a Non-linear Graph

The x-axis is horizontal and the y-axis is vertical.

The data on the x-axis (linear) in line graphs is usually constant.

The data on the y-axis in line graphs is variable (changing), i.e., either increasing or decreasing.

 

Parts of a Line Graph

We need to draw and label graphs properly so that the data can be read and interpreted accurately.

  • The title or heading gives us an idea of what the graph is all about.
     
  • The horizontal and vertical labels indicate the information being displayed.
     
  • The scale, which is the range of values on the x-axis and y-axis, tells us the quantity of the information being displayed.
     
  • The dots or points on the graph, shows the information that is being compared.
  • The lines joining the dots, shows the pattern.

In the above graph the dots or points follow a regular pattern (2, 4, 6, …) which results in  a straight line.  A straight line indicates a linear graph.  The line in the graph above has an upward slope, which indicates it is showing an increase in the data.

Drawing Graphs

We can draw graphs from information given.

Example

The table below shows the total monthly car sales at SA Motors over a year.  We will use this information and follow the five steps below the table for drawing a line graph.

CAR SALES FOR ONE YEAR

Month

Cars Sold

January

13

February

25

March

30

April

22

May

47

June

29

July

36

August

40

September

52

October

44

November

56

December

65

Step 1

Identify the range of values.  In this graph there are two sets of values:

i)  Months of the year:  January to December

ii)  Number of cars sold:  smallest (13) to biggest (65)

Step 2

Select a scale, for example, in this graph, one block = 10 cars.

Step 3

Label the graph.

i)  The x-axis (horizontal)  in this graph is months of the year (constant – stays the same)

ii)  The y-axis (vertical) in this graph number of cars sold (variable – changes)

Step 4

Plot the numbers or values using dots or points, then join the points or dots.

Step 5

Remember to give your graph a suitable title or heading, for example, for this graph, ‘Monthly Car Sales Over a 1 Year Period’.

The information is now clearly visual, so it becomes easier to study and interpret the graph by answering questions.

Example

a)  How many cars were sold altogether in one year?

b)  In which month was the most cars sold and how many cars were sold in this month?

c)  Why do you think so many cars were sold in this month?

d)  Why do you think so few cars were sold in January?

e)  Is this a linear or non-linear graph?  Give a reason for your answer.

Answers

a)  460 cars were sold in one year.

b)  December – 65 cars.

c)  Answers will vary.
     Possible answer could be: Many people get bonuses and save up the entire year.
           
d)  Answers will vary.
     Possible answer could be:  Many people spend a lot during the festive season
     and experience financial problems during the start of the new year.

e)  Non-linear graph, because the number of cars sold is not constant.

 

ACTIVITIES 

Activity 1

Interpreting Graphs

Study the graphs below and then answer the questions that follow:

  1. The graphs below shows the distance travelled by a car in 10 hours.

    1. What is the title of the graph?
    2. What is the scale on the y-axis?
    3. What does the x-axis represent?
    4. What unit of measurement is represented on the y-axis?
    5. How long will it take to travel 120 km?
    6. After travelling for three hours, how many kilometres would you have travelled?
    7. Is this a linear or non-linear graph? Give a reason for your answer.
    8. Does the upward slope of the graph indicate an increase or decrease over time?
  2. The graph below shows the annual rainfall in Johannesburg.

    1. What is the title of the graph?
    2. What is the label on the y-axis?
    3. What is the highest annual rainfall and in which month was it recorded?
    4. What does each block on the y-axis represent?
    5. Is this a linear or non-linear graph? Give a reason for your answer.
    6. How many dots or points are plotted on the graph?
    7. What is the scale on the y-axis?
  3. The graph below shows the decrease in hotdog sales over a week.

    1. What is the label on the horizontal axis?
    2. What is the difference in the number of hotdogs sold on Monday and Sunday?
    3. Is this a linear or non-linear graph? Give a reason for your answer.
    4. What does this graph represent?
    5. What is the scale on the y-axis?

Activity 2

Drawing Graphs
  1. Use the information provided in the table below to draw a graph to show the distance cycled by a group of friends over a ten day training programme. Remember to follow the five steps to drawing a graph.

    Time (days) 1 2 3 4 5 6 7 8 9 10
    Distance (km) 10 20 30 40 50 60 70 80 90 100
  2. Click on the link below for graph paper.

    Graph Paper

  3. Plot the following minimum and maximum average temperatures per annum for Durban on a the same graph. Remember to use a key to show your minimum and maximum temperatures.

    Months Jan Feb Mar April May June
    Minimum Temperature (℃) 22 ℃ 21 ℃ 20 ℃ 18 ℃ 15 ℃ 12 ℃
    Maximum Temperature (℃) 35 ℃ 33 ℃ 32 ℃ 30 ℃ 24 ℃ 22 ℃
    Months July Aug Sept Oct Nov Dec
    Minimum Temperature (℃) 10 ℃ 14 ℃ 15 ℃ 16 ℃ 19 ℃ 23 ℃
    Maximum Temperature (℃) 20 ℃ 25 ℃ 26 ℃ 28 ℃ 31 ℃ 34 ℃