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Drawing reciprocal graphs

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

New
New

Drawing reciprocal graphs

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

Lesson details

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.

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.
Teacher tip

Equipment

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

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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

Assessment exit quiz

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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)

Lesson appears in

UnitMaths / Non-linear graphs

Maths

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