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      Drawing reciprocal graphs

      Lesson details

      Learning outcome

      I can generate coordinate pairs for a reciprocal graph from its equation and then draw the graph.

      Key learning points

      1. Inverse proportion graphs are reciprocal graphs.
      2. A table of values can be useful to identify coordinate pairs which satisfy the equation.
      3. By substituting the values for x, you can calculate corresponding values for y.
      4. If used correctly, your calculator can be a powerful tool to speed up calculations.

      Keywords

      • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

      Common misconception

      $$1 / 0$$ evaluates to give $$0$$

      Get pupils to consider what happens when $$x=1/2$$, $$x=1/3$$, $$x=1/4$$ etc. This will help them spot the role of the $$y$$ axis as asymptote for themselves.

      Teacher tip

      Making connections is really important when learning mathematics. Linking the fact that $$y=4/x$$ has no $$x$$-intercept whereas $$y=4/x$$ $$-2$$ does because $$4/x=0$$ has no solution whereas $$4/x$$ $$-2=0$$ has one is empowering to students.

      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.
      $$1\over7$$ is the __________ of $$7$$

      divisor
      factor
      inverse
      Correct answer: reciprocal

      Q2.
      What is the value of $$y$$ when $$x=5$$ in the equation $$y=15x$$?

      Correct Answer: 75, y=75

      Q3.
      What is the value of $$y$$ when $$x=5$$ in the equation $$y={15\over{x}}$$?

      Correct Answer: 3, y=3

      Q4.
      What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y=6x$$?

      12
      6
      Correct answer: 3
      -3

      Q5.
      What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y={6\over{x}}$$?

      36
      Correct answer: 12
      6
      3
      -3

      Q6.
      What is the value of $$y$$ when $$x=-{1\over{2}}$$ in the equation $$y={6\over{x}}$$? A calculator might be useful to check your calculation here.

      Correct answer: -12
      -3
      3
      12

      6 Questions

      Q1.
      __________ graphs can have the form $$y={k\over{x}}$$

      Cubic
      Linear
      Quadratic
      Correct answer: Reciprocal

      Q2.
      Which coordinate pairs will appear in the graph of $$y={30\over{x}}$$?

      Correct answer: (1, 30)
      Correct answer: (30, 1)
      Correct answer: (2, 15)
      (3, 15)
      (6, 10)

      Q3.
      Which coordinate pairs will appear in the graph of $$y={45\over{x}}$$ ?

      Correct answer: (-9, -5)
      (-9, 5)
      (0, 45)
      (-5, 9)
      Correct answer: (-5, -9)

      Q4.
      Laura say this is not the graph of a reciprocal equation. How can you tell Laura is correct?

      An image in a quiz
      The $$y$$ values should be positive, not negative.
      It does not intercept the $$x$$ or $$y$$ axis.
      Correct answer: The curves should be in diagonally opposite quadrants.
      It is the graph of a reciprocal equation.

      Q5.
      Which of these reciprocal graphs will intercept the $$x$$ axis?

      $$y={1\over{x}}$$
      $$y=-{1\over{x}}$$
      Correct answer: $$y={1\over{x}}+1$$
      Correct answer: $$y={1\over{x}}-1$$
      $$y={0.1\over{x}}$$

      Q6.
      Which coordinate pair is the $$x$$ intercept for the graph of $$y={42\over{x}}-6$$ ?

      Correct answer: (7, 0)
      (6, 0)
      (0, -6)
      (-6, 0)
      (-7, 0)

      To help you plan your 10 maths lesson on: Drawing reciprocal graphs, download all teaching resources for free and adapt to suit your pupils' needs...