9.1 Direct proportion on graphs - Schudio · Company B shows direct proportion as the graph is a...

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9.1 Direct proportion on graphs 1 Are litres and pints in direct proportion? Explain.

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2 A scientist tests the electrical resistance of different lengths of copper wire and gets these results.

a Are resistance and length in direct proportion? Explain.

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b Use the graph to work out the resistance of a wire with length:

i 5 m ......................

ii 12 m ......................

iii 20 m. ......................

c Use the graph to work out the length of a wire with resistance:

i 0.03 ohms ......................

ii 0.20 ohms. ......................


3 The two tables show the cost of hiring a car from two different companies. Company A Number of days 2 5 7

Cost (£) 41 102.50 130

Company B Number of days 2 5 7

Cost (£) 38 95 133

a Plot graphs for these two companies and use your results to identify if either company uses direct proportion between the number of days and the cost.

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b Work out the cost of hiring a car from Company B for 8 days. ......................

c Is it possible to work out the cost of hiring a car from company A for 8 days? Explain.

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9.1 Direct proportion on graphs 1 A bike hire company charges a deposit and an hourly rate.

Some of the charges are shown in the table. Time (hours) 1.5 2.5 5

Cost (£) 16.60 19 25

a Draw a graph to show this information.

b How much is the deposit? ..........................

c What is the hourly rate? ..........................

d When the bike is returned, the deposit is refunded. Does this mean time and cost are in direct proportion? Explain.

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2 Are these measures directly proportional? Explain.

a The edge length of a regular pentagon and its perimeter.

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b The edge length of a square and its area.

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c The base length of an isosceles triangle and its area, given that its perpendicular height is three times its base length.

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3 A cleaning company charges £50 for the first hour. After that it charges £12 every half hour. However, if they work for 3 hours or more, they charge all hours, including the first, at £30 per hour.

a Draw a graph showing the costs from 0 to 5 hours of work.

b When is the amount of work in direct proportion to the cost?

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9.1 Direct proportion on graphs 1 Here is a graph.

a Is the graph a straight line? ......................

b Does the graph pass through the point with coordinates (0, 0)? ......................

c When the value on the horizontal axis doubles, does the value on the vertical axis double? ......................

d Are the quantities on the horizontal axis and the vertical axis in direct proportion? ......................

2 Here are four graphs.

I II III IV

a Which two graphs show that one variable is in direct proportion to the other? ......................

b Explain how you know that the other two graphs do not show direct proportion.

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3 The table shows some information about the number of car doors a machine can attach over time.

Time, t (hours) 0 2 4 6

Doors attached, d 0 40 80 120

a Check that when t = 0, then d = 0.

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b Show that as t doubles, d also doubles.

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c Show that as t triples, d also triples.

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d Plot the points onto the graph.

e Join the points. Do they make a straight line? ......................

f Decide whether each statement is true or false.

i When one variable is zero, the other is also zero. ......................

ii When one variable doubles, the other also doubles. ......................

iii The graph is a straight line through (0, 0). ......................

g Are time and the number of doors attached in direct proportion? Use your answers from part f to explain.

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9.1 Direct proportion on graphs Core 1 Yes, they are directly proportional. Zero litres equals zero pints and if you double the number of litres you will double the number of pints.

2 a Yes, the graph is a straight line that passes through (0, 0).

b i 0.11 ii 0.26 iii 0.44

c i 1.25 m ii 9 m

3 a

Company B shows direct proportion as the graph is a straight line that passes through (0, 0).

b £152

c The cost for company A cannot be worked out for 8 days’ hire as the relationship is not one of direct proportion.

Depth 1 a b £13 c £2.40

d Yes, because the deposit is returned so the graph would be a straight line through (0, 0).

2 a Yes, if the edge length is a then the perimeter is 5a. This will produce a straight-line graph through (0, 0).

b No, as the area of the square will be the edge length squared, which would not produce a straight- line graph.


c No, as the area of the triangle will be 1.5 times the edge length squared, which would not produce a straight-line graph.

3 a b When the work time is 3 hours and over.

Support 1 a Yes, it is a straight line.

b Yes, it passes through (0, 0).

c Yes, the values double. On the horizontal axis 3 doubles to 6 and on the vertical 5 doubles to 10.

d Yes, they are in direct proportion.

2 a graphs III and IV b Graph I does not go through (0, 0) and graph II is not a straight line.

3 a Yes – evidence from the table.

b Yes, time 2 doubles to 4 and doors 40 doubles to 80.

c Yes, time, 2 triples to 6 and doors, 40 doubles to 120.

d See graph

e Yes.

f i True ii True iii True

g Yes, time and number of doors are in direct proportion as the graph is a straight line through (0, 0).

Time, t (hours) 0

Doors attached, d 0

9.1 Direct proportion on graphs - Schudio · Company B shows direct proportion as the graph is a...

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