Conversion graphs
Graphs are often used in everyday life to give information about how two quantities are related.
A conversion graph is a straight-line graph that shows the relationship between two units of measurement. It can be used to convert from one unit to the other.
Example
The graph shows the relationship between litres (l) and gallons (g).
A can holds 10 litres of paint. How many gallons is this?
Solution:
Find 10 litres on the horizontal axis and draw a vertical line to meet the line.
From there, draw a horizontal line to meet the vertical axis.
Read the value shown on the axis.
Each small square = 0.1 gallons.
The reading here is 2.2 gallons.
Example
Use the graph to find how many gallons is equivalent to 40 litres.
Solution:
The graph does not go up to 40 litres.
But we know from the last example that 10 litres is equivalent to 2.2 litres.
Therefore 40 litres is equivalent to 2.2 x 4 gallons.
2.2 x 4 = 8.8 gallons
Question
Use the conversion graph above to find how many litres are equivalent to 3.5 gallons.
Find 3.5 gallons on the vertical axis and draw a horizontal line to meet the black line.
From there, draw a vertical line down to the horizontal axis and read off the value.
One small square = 1 litre
The reading is at 16 litres
Answer: 3.5 gallons is equivalent to 16 litres.
Travel graphs
A travel graph is a line graph which describes a journey – it shows how distance changes with time.
Time is always represented on the x-axis and distance on the y-axis.
The distance is always distance from a particular place and the time is the time from the start of the journey.
Example
Emily cycles from her house to her Nanny’s.
The graph below shows her journey.
The journey is in three parts.
Blue line – this represents the first 30 minutes of the journey. Emily is 5 km from home after 30 minutes.
Red line – the time has increased by 5 minutes, but the distance has not increased. This means Emily stopped cycling for 5 minutes.
Green line – this represents the last 25 minutes of the journey. The whole journey has taken 60 minutes and Emily is now 12 km from home.
Question
What was Emily’s speed, in kilometres per hour (km/hr), over the first part of the journey?
Did Emily cycle faster before or after she stopped for 5 minutes?
Answer
- Emily cycled 5km in 30 minutes. In 60 minutes, she would cycle 10 km so her speed over the first part of the journey is 10 km/hr.
You could work out the speed after the stop but there is no need to do that.
- Look at the blue line.
In the first 15 minutes, Emily has cycled 2.5 km.
Look at the green line.
In the first 15 minutes of this part of the journey, Emily has cycled just over 4 km – more distance over the same time.
Emily cycled faster after she stopped for 5 minutes.
Note that the green line is steeper than the blue one.
Test yourself
More on M5: Handling data
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