Starter:

A) y = x + 1

B) y = x – 1

Real Life Graphs

• Objective: To understand how graphs are used to show relationships between variables

Must: Read table accurately

Could: Interpret graphs

Should: Draw conclusion from Velocity graphs

Plotting graphs – using a table of values

When we plot a graph we usually start with a table of values.

The values in the table usually come from a formula or equation or from an observation or experiment.

For example, a car hire company charges £30 to hire a car and then £25 for each day that the car is hired.

This would give us the following table of values:

The cost of the car hire depends on the number of days. The number of days must therefore go in the top row.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155

Plotting graphs – choosing a scale

The next step is to choose a suitable scale for the axes.

Look at the values that we need to plot.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155

The number of days will go along the horizontal axis.

The numbers range from 1 to 5.

A suitable scale would be 2 units for each day.

The cost will go along the vertical axis.

The cost ranges from 55 to 155.

A suitable scale would be 1 unit for each £10. We could start the scale at £30.

Plotting graphs – drawing the axes

We then have to draw the axes using our chosen scale.

We will need at least 10 squares for the horizontal axis and 13 squares for the vertical axis.

When the scale does not start at 0 we must show this with a zigzag at the start of the axis.

Number the axes.

30405060708090

100110120130140150

0 1 2 3 4 5

Label the axes, remembering to include units, if necessary.

Number of days

Cos

t (£

)

Plotting graphs – plotting the points

Use the table of values to plot the points on the graph.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155

00

30405060708090

100110120130140150

1 2 3 4 5

Number of days

Cos

t (£

)

It is most accurate to use a small cross for each point.

If appropriate, join the points together using a ruler.

Lastly, don’t forget to give the graph a title.

Cost of car hire

Science experiment

Mass of object moving down ramp (grams)

Time taken for object to move down ramp (seconds)

100

4

150

7

200

12

250

17

A group of pupils are doing an experiment to explore the effect of friction on an object moving down a ramp.

They attach weights of different mass to the object and time how long the object takes to reach the bottom of the ramp.

They put their results in a table and use the table to plot a graph of their results.

Science experiment

Mass of object moving down ramp (grams)

Time taken for object to move down ramp (seconds)

100

4

150

7

200

12

250

17

Mass of object (grams)

0

4

8

12

16

20

0 50 100 150 200 250 300

Tim

e ta

ken

(se

con

ds)

We can join the points using straight lines.

Do the intermediate points have any practical significance?

How could we make the graph more accurate?

Travel Graphs

A travel graph gives information about how someone or something has travelled over a given time period. It is also called a distance–time graph.

You can find the average speed from a distance–time graph by using the formula:

average speed = total distance travelled total time taken

You always work out the distance travelled in 1 hour to get the speed in kilometres per hour (km/h) or miles per hour (mph).

Distance-time graphsIn a distance-time graph the horizontal axis shows time and the vertical axis shows distance.

For example, John takes his car to visit a friend. There are three parts to the journey:

John drives at constant speed for 30 minutes until he reaches his friend’s house 20 miles away.

He stays at his friend’s house for 45 minutes.

He then drives home at a constant speed and arrives 45 minutes later.

0

time (mins)

dist

ance

(m

iles)

15 30 45 60 75 90 105 120

5

10

15

20

0