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18.5 Direct proportion

18.5 Direct proportion

When two variables are in direct proportion, the graph of the relation is a straight line through
the origin.

It is easy to !nd the equation of the line. "en the equation can be used to !nd missing values
algebraically.

Worked example 18.5

The cost of petrol is $2.85 per litre.
a Write a formula for the cost in dollars (C) of L litres.
b Show that the graph of this formula passes through the origin.
c Use the formula to find the number of litres you can buy for $500.

a C = 2.85 L Multiply the number of litres by 2.85 to find the cost,
in dollars.

b If L = 0 then C = 0 The origin is (0, 0).
500 Substitute C = 500 into the formula and rearrange to
c 500 = 2.85 L A L = 285 = 175.44 find L.
.
You can buy 175.44 litres.

) Exercise 18.5

1 Metal wire costs $6.20 per metre.
a Draw a graph to show the cost of up to 10 metres.
b Work out the gradient of the graph.
c Write down a formula for the cost in dollars (C) of M metres.
d Use the formula to find: i the cost of 12.5 metres ii how many metres you can buy for $200.

2 A photocopier can copy 16 pages per minute.
a Write down a formula for the number of pages (p) that can be photocopied in m minutes.
b Draw a graph to show the number of pages that can be photocopied in up to 5 minutes.
c Work out the gradient of the graph.
d Use the formula to find:
1
i how many pages can be copied in 7 minutes ii the time to photocopy 312 pages.
2
3 A packet of 500 sheets of paper has mass 2.5 kg.
a Find the mass, in grams, of one sheet of paper.
b Write down a formula for the mass (m), in grams, of n sheets of paper.
c Draw a graph to show the mass, in grams, of up to 500 sheets of paper.
d Mia weighs some sheets of paper. The mass is 0.385 kg. How many sheets are there?
4 Greg buys 83 litres of fuel. It costs him $346.11.
a Work out the cost of one litre of fuel.
b Draw a graph to show the cost of up to 100 litres of fuel.
c Write down the gradient of the graph.
d How many litres can Greg buy for $500?

18 Graphs 18 Graphs 173