top of page

11.7 Proportion and Graphs

GCSE Maths Foundation · Edexcel · Chapter 11: Ratio and Proportion

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: graphs of direct proportion, y = kx, and conversion graphs. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Recognise direct proportion from a table or a graph
  • Draw and use a straight-line graph through the origin
  • Find and use the value of k in y = kx
  • Read and use conversion graphs

Key words

  • Origin: The point (0, 0), where the axes cross.
  • Direct proportion graph: A straight line that passes through the origin.
  • Constant k: The constant of proportionality: the number k in y = kx. It is y ÷ x for every pair of values, and is the gradient of the line.
  • Conversion graph: A straight-line graph used to change between two units, such as miles and kilometres.

Graphs of direct proportion

If two quantities are in direct proportion, their graph is a straight line through the origin. 0 kg of plums cost £0, and each extra kilogram adds the same amount.

  • Cost (£); 0 0; 1 3; 2 6; 3 9; 4 12; 5 15

Worked example: reading the graph

Use the graph to find the mass of plums you can buy for £12.
Go across from £12 to the line, then down: 4 kg. Check: 12 ÷ 3 = 4 ✓

Answer: 4 kg

Is it direct proportion?

In a table, divide each y by its x. If you always get the same number, it is direct proportion. On a graph, the line must be straight and go through (0, 0).

Worked example: checking a table

x: 2, 5, 8. y: 7, 17.5, 28. Is y in direct proportion to x?
7 ÷ 2 = 3.5, 17.5 ÷ 5 = 3.5, 28 ÷ 8 = 3.5. All the same.

Answer: Yes, y = 3.5x

Using y = kx

Direct proportion can be written as a formula y = kx. Find k from one pair of values: k = y ÷ x. On the graph, k is the gradient: how much y goes up when x goes up by 1.

Worked example: paint

The cost, £C, of paint is in direct proportion to the number of litres, L. 5 litres cost £35.
(a) Write a formula. k = 35 ÷ 5 = 7, so C = 7L
(b) Find the cost of 12 litres. C = 7 × 12 = 84

Answer: (a) C = 7L (b) £84

Conversion graphs

Read up from one axis to the line, then across to the other axis. For values off the graph, use proportion: scale up a value you can read.

Worked example: beyond the graph

Use the graph to change 100 miles into kilometres.
From the graph, 25 miles = 40 km. 100 miles = 4 × 25 miles, so 4 × 40 = 160 km

Answer: 160 km

Common mistakes

  • Thinking every straight line shows direct proportion. It must also pass through (0, 0).
  • Checking only that y goes up by the same amount each time. Divide y by x instead.
  • Misreading the scale. Work out what one small square is worth before you read a value.
  • Reading the wrong axis. Start on the axis of the unit you are given and finish on the other one.

Revision questions

Try these, then check your answers below each one.

Question 1. Which of these describes the graph of two quantities in direct proportion? (Choose from: A straight line through the origin, Any straight line, A curve through the origin, A horizontal line.)

Answer: A straight line through the origin

Working: Direct proportion gives a straight line that passes through (0, 0).

Question 2. y = kx. The graph of y against x passes through (4, 18). What is k?

Answer: 4.5

Working: k = 18 ÷ 4 = 4.5.

Question 3. True or false? This table shows y in direct proportion to x: x = 2, 3, 5 and y = 6, 9, 15.

Answer: True

Working: 6 ÷ 2 = 9 ÷ 3 = 15 ÷ 5 = 3. The ratio is constant, so true.

Related lessons

Continue in the full course

This lesson is section 11.7 (EGCMF1107) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

bottom of page