Direct proportion graphs

The Maths Habit Handout to print

Taxi A charges £2 a mile.
Taxi B charges £5 to start,
then £1.50 a mile.
Which taxi would you choose?

Taxi A for trips under 10 miles

Taxi B for trips over 10 miles

At 10 miles both cost £20

Origin
The point (0, 0), where the axes cross.

The cost of hiring a bike is directly proportional to the number of hours. 2 hours costs £12.

Hours1234
Cost (£)12

012340102030HoursCost (£)

A straight line through (0, 0)

5 litres of paint cost £20.
Draw the graph. Find the cost of 3 litres.

Litres12345
Cost (£)48121620
01234505101520LitresCost (£)
Answer£12

4 kg of sand costs £6.
Draw the graph. Find the cost of 3 kg.

kg1234
Cost (£)1.5034.506
012340123456KilogramsCost (£)
Answer£4.50

5 litres of paint cost £20.
Draw the graph. Find the cost of 3 litres.

Litres12345
Cost (£)48121620
01234505101520LitresCost (£)
Answer£12

8 pens cost £10.
Draw the graph. Find the cost of 6 pens.

Pens2468
Cost (£)2.5057.5010
024680246810PensCost (£)
Answer£7.50

5 litres of paint cost £20.
Draw the graph. Find the cost of 3 litres.

Litres12345
Cost (£)48121620
01234505101520LitresCost (£)
Answer£12

6 m of rope costs £9. Draw the graph. Find the cost of 4 m.

Metres246
Cost (£)369
01234560246810MetresCost (£)
Answer£6

5 litres of paint cost £20.
Draw the graph. Find the cost of 3 litres.

Litres12345
Cost (£)48121620
01234505101520LitresCost (£)
Answer£12

4 hours of parking cost £7. Draw the graph. Find the cost of 3 hours.

Hours1234
Cost (£)1.753.505.257
0123402468HoursCost (£)
Answer£5.25

5 litres of paint cost £20.
Draw the graph. Find the cost of 3 litres.

Litres12345
Cost (£)48121620
01234505101520LitresCost (£)
Answer£12

5 kg of flour costs £4. Draw the graph. How many kg for £2.40?

kg12345
Cost (£)0.801.602.403.204
01234501234kgCost (£)
Answer3 kg

Direct proportion graphs worksheet, page 1

Answer sheet

  1. A graph for changing pounds to euros goes through (20, 23). How many euros is £50?

    57.50 euros

  2. A straight line goes through (4, 9) and (10, 22). Is it direct proportion? How do you know?

    No

  3. Graph A is a straight line through (0, 3) and (6, 15). Graph B is a curve through (0, 0) and (2, 4). Graph C is a straight line through (0, 0) and (5, 8). Which graph shows direct proportion?

    C

  1. Which graph shows direct proportion?

    B
    xyAxyBxyC

  2. The graph shows the cost of sand. Use it to find the cost of 6 kg.

    £15
    02468481216200Mass (kg)Cost (£)

  3. A straight line goes through (2, 6) and (5, 14). Does it show direct proportion? Explain.

    No: 6 ÷ 2 = 3, 14 ÷ 5 = 2.8
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