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18 Graphs

What can you say about the equation y = 0.5x + 5? Key words
You should recognise it as the equation of a straight line. Make sure you learn and

To draw the line you need to !nd some points. Start with a table understand these key words:
of values. gradient

x −20 −15 −10 −5 0 5 10 15 20 coefficient
direct proportion
0.5x + 5 −5 −2.5 0 2.5 5 7.5 10 12.5 15

Now you can plot these points on a graph and draw a straight line through them.

y
15
10
5

0 x
–20–15 –10 –5 5 10 15 20
–5
–10

But what would you use a linear graph for?
Here are some practical examples.

Population of a country f Fuel in a vehicle
P 60 f = 60 – 0.08d
Population (millions) 20 P = 0.5t + 20 Fuel (litres) 40
25
50
15
30
20
10
5
0 10 0
0 2 4 6 8 10 t 0 100 200300 400 500 d
Years Distance (km)

T Temperature 40 l Rectangle with
Temperature (°C) 1000 T = 1000 + 25s Length (cm) 30 l = 50 – w
of an engine
perimeter 1 m
2000
20

0 10 0
0 2 4 6 8 10 s 0 10 20 30 40 50 w
Time (seconds) Width (cm)

From these, you can see that the variables do not have to be x and y. You can use any letters.
In this unit you will learn more about interpreting, drawing and using all sorts of graphs.

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