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Year 11
Higher

Finding the constant of proportionality for direct proportion

I can use the general form for a directly proportional relationship to find k.

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New
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Year 11
Higher

Finding the constant of proportionality for direct proportion

I can use the general form for a directly proportional relationship to find k.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Direct proportion equations are of the form y = kx
  2. k is the constant of proportionality and it is also the gradient of the graph.
  3. To find the gradient, k, you can use two sets of coordinates (pairs of values).

Keywords

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

Common misconception

Failing to recognise that x/2 is the same as 1/2 × x and therefore shows a directly proportional relationship where the value of k is 1/2.

It is useful to go back to looking at unit fractions. E.g. 2/3 = 1/3 × 2 and 7/9 = 1/9 × 7, etc. And, then look at algebraic terms leading up to for example, 2x/3. 'What is the the multiplier?'

Using mini-whiteboards ask students to come up with their own examples and non-examples of equations representing direct proportion.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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6 Questions

Q1.
Any non-zero number multiplied by its is equal to 1.
additive inverse
Correct answer: reciprocal
difference
Q2.
Which of the following tables show direct proportion?
An image in a quiz
Correct answer: a
Correct answer: b
c
Correct answer: d
Q3.
Match the numbers to their reciprocals.
Correct Answer:$$1\over8$$,8

8

Correct Answer:$$8\over3$$,$$3\over8$$

$$3\over8$$

Correct Answer:$$1\over3$$,3

3

Correct Answer:6,$$1\over6$$

$$1\over6$$

Correct Answer:$$6\over5$$,$$5\over6$$

$$5\over6$$

Q4.
Decide which of the following would share a directly proportional relationship.
The time taken to make 10 000 items and the number of machines
Correct answer: The height of a staircase and the number of stairs
Correct answer: The cost to wallpaper a room and the size of the room
The number of sweets in a bag and the number of people sharing it
Q5.
$$h$$ is directly proportional to $$g$$. When $$g$$ = 17, $$h$$ = 93.5. Find $$h$$ when $$g$$ = 25.
Correct Answer: 137.5
Q6.
$$h$$ is directly proportional to $$g$$. When $$h$$ = 17, $$g$$ = 93.5. Find $$g$$ when $$h$$ = 60.5.
Correct Answer: 11, eleven

Exit quiz

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6 Questions

Q1.
When dealing with equations of direct proportion we use the equation $$y = kx$$. What does $$k$$ represent?
the additive relationship between $$x$$ and $$y$$
the difference between $$x$$ and $$y$$
Correct answer: the constant of proportionality
Q2.
Which of the following equations represent $$y$$ being directly proportional to some form of $$x$$?
Correct answer: $$y=3x$$
Correct answer: $$y=\sqrt{3}x$$
$$y=3x+1$$
$$y=3\sqrt{x}$$
Correct answer: $$y={x\over3}$$
Q3.
Match each equation to its correct value of $$k$$.
Correct Answer:$$y={x\over6}$$,$$1\over6$$

$$1\over6$$

Correct Answer:$$y={\sqrt6{x}}$$,$${\sqrt6}$$

$${\sqrt6}$$

Correct Answer:$$y={5x\over6}$$,$$5\over6$$

$$5\over6$$

Correct Answer:$$y={\sqrt5{x}}$$,$${\sqrt5}$$

$${\sqrt5}$$

Correct Answer:$$y={6x\over5}$$,$$6\over5$$

$$6\over5$$

Q4.
$$y$$ is directly proportional to $$x$$. When $$x$$ = 13, $$y$$ = 52. Write an equation connecting $$x$$ and $$y$$.
$$y=x+4$$
Correct answer: $$y=4x$$
$$y=x-4$$
$$y=4x+4$$
Q5.
$$y$$ is directly proportional to $$x$$. When $$x$$ = 6, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 14.
Correct Answer: 30.8
Q6.
$$y$$ is directly proportional to $$x$$. When $$x$$ = 6, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 123.2.
Correct Answer: 56