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      Graphing direct proportion

      I can recognise direct proportion graphically and be able to identify features of the graph.

      Lesson 13 of 16
      New
      New
      • Year 8

      Graphing direct proportion

      I can recognise direct proportion graphically and be able to identify features of the graph.

      Lesson details

      Key learning points

      1. Direct proportion can be recognised graphically.
      2. A direct proportion graph is always a straight line.
      3. The origin is always a point on a direct proportion graph.
      4. The gradient tells us the constant of proportionality.
      5. Using these features it is possible to identify direct proportion graphs.

      Keywords

      • Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.

      Common misconception

      Assuming that any graph with a constant positive gradient represents variables that are in direct proportion.

      Encourage the useful check of reading a pairs of values from the graph, doubling one of them and checking the graph to see if the other variable has doubled. If it has it shows a directly proportional relationship if not it doesn't.

      Using mini-whiteboards, for example, ask students to sketch their own examples and non-examples of graphs showing direct proportion.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Two variables are in direct if they have a constant multiplicative relationship.

      Correct Answer: proportion

      Q2.
      Which of the following show a directly proportional relationship between A and B?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz

      Q3.
      A and B are directly proportional. The missing value of B is .

      An image in a quiz
      Correct Answer: 36

      Q4.
      A and B are directly proportional. The missing value of B is .

      An image in a quiz
      Correct Answer: 90

      Q5.
      The graph shows the relationship between cost and number of boxes bought. Can you spend exactly £5 on boxes?

      An image in a quiz
      Correct answer: No, reading off the graph at £5 shows you can buy between 2 and 3 boxes.
      Yes, reading off the graph at £5 shows you can buy exactly 3 boxes.

      Q6.
      This graph shows that A and B are in direct proportion. The proportional relationship between A and B is B = A × .

      An image in a quiz
      Correct Answer: 3

      Assessment exit quiz

      6 Questions

      Q1.
      Graphs showing direct proportion have a positive gradient with an of 0.

      Correct Answer: intercept

      Q2.
      Which of the following graphs does NOT show direct proportion?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      Q3.
      Which tables show that A and B are in direct proportion?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz

      Q4.
      The constant of proportionality represented by this graph is .

      An image in a quiz
      Correct Answer: 4, four

      Q5.
      Which of the following is NOT true of this graph?

      An image in a quiz
      The constant of proportionality is $$3$$.
      Correct answer: The equation of the line is $$x = 3y$$.
      The gradient of the line is $$3$$.
      The graph has an intercept of zero.
      Correct answer: The graph does not show a directly proportional relationship.

      Q6.
      What are the key features of a graph showing direct proportion?

      It has a negative gradient.
      Correct answer: It has an intercept of zero.
      Correct answer: It has a constant positive gradient.
      The intercept can be 0.1
      It has a gradient of 0

      Lesson appears in

      UnitMaths / Understanding multiplicative relationships: percentages and proportionality