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Graphs showing inverse proportion

I can recognise inverse proportion graphically and can interpret graphs that illustrate inverse proportion.

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Lesson 7 of 11

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Year 10

Graphs showing inverse proportion

I can recognise inverse proportion graphically and can interpret graphs that illustrate inverse proportion.

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Key learning points

Inverse proportion can be recognised graphically.
The equation of an inverse proportion graph is of the form y = k/x
An alternative way of writing the equation is y α 1/x

Keywords

Inverse proportion - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Common misconception

Solutions for context-based problem can be listed as coordinate pairs with units e.g. 6 workers, 60 hours.

Solutions should always be fully interpreted in relation to the context e.g. It would take 6 workers 60 hours to paint the building.

k is used in the notation to prepare pupils for the Year 11 unit where k is formally referred to as the constant of proportionality.

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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).

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Prior knowledge starter quiz

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6 Questions

Q1.
If it takes 2 hours to walk 6 miles, 3 hours to walk 9 miles, and 4 hours to walk 12 miles then the variables time and distance are said to ...

Correct answer: be in direct proportion to each other.

be unrelated.

have a changing rate of change.

Q2.
Which of these graphs shows a directly proportional relationship?

Correct Answer: An image in a quiz

Q3.
This time distance graph shows the relationship between the hours walked and the distance travelled in miles. What do the coordinates (5, 20) show?

It takes 5 hours to walk 20 km.

It takes 20 hours to walk 5 km.

Correct answer: It takes 5 hours to walk 20 miles.

It takes 20 hours to walk 5 miles.

Q4.
What is the equation of the line in this distance-time graph? Use $$d$$ for distance travelled and $$t$$ for time taken.

$$d=5t$$

$$t=5d$$

Correct answer: $$d=4t$$

$$4d=t$$

$$d=t+4$$

Q5.
For the equation $$s={30\over{t}}$$, when $$t=7.5$$, $$s=$$ .

Correct Answer: 4, s=4

Q6.
For the equation $$s={30\over{t}}$$, when $$s=7.5$$, $$t=$$

Correct Answer: 4, t=4

Assessment exit quiz

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6 Questions

Q1.
When two variables are indirectly proportional, as one variable increases the other ...

increases.

Correct answer: decreases.

remains constant.

Q2.
Inversely proportional relationships are modelled by the relationship ...

$$ky=x$$

$$y=kx$$

$$y={x\over{k}}$$

Correct answer: $$y={k\over{x}}$$

Q3.
Which of these graphs shows a relationship of indirect proportion?

Correct Answer: An image in a quiz

Q4.
Why can this not be a graph of indirect proportion?

Correct answer: Indirect proportion graphs do not intersect either axis.

It is not a straight line.

It is decreasing as the horizontal variable decreases.

Correct answer: Indirect graphs have the form $$y={k\over{x}}$$ , dividing by zero is undefined.

Q5.
This graph plots the time taken ($$t$$) in days for a varying number of people ($$p$$) to dig a hole. How long would it take 3 people?

5 people

Correct answer: It would take 3 people 5 days to dig the hole.

It would take 5 people 3 days to dig the hole.

Q6.
This graph shows the relationship between people and time required to build a wall. The point marked shows that 10 people would take 3 days. It would take 3 people days to build the wall.

Correct Answer: 10, Ten

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UnitMaths / Linear graphs

Maths

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Graphs showing inverse proportion

Graphs showing inverse proportion

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.If it takes 2 hours to walk 6 miles, 3 hours to walk 9 miles, and 4 hours to walk 12 miles then the variables time and distance are said to ...

Q2.Which of these graphs shows a directly proportional relationship?

Q3.This time distance graph shows the relationship between the hours walked and the distance travelled in miles. What do the coordinates (5, 20) show?

Q4.What is the equation of the line in this distance-time graph? Use $$d$$ for distance travelled and $$t$$ for time taken.

Q5.For the equation $$s={30\over{t}}$$, when $$t=7.5$$, $$s=$$ .

Q6.For the equation $$s={30\over{t}}$$, when $$s=7.5$$, $$t=$$

Assessment exit quiz

6 Questions

Q1.When two variables are indirectly proportional, as one variable increases the other ...

Q2.Inversely proportional relationships are modelled by the relationship ...

Q3.Which of these graphs shows a relationship of indirect proportion?

Q4.Why can this not be a graph of indirect proportion?

Q5.This graph plots the time taken ($$t$$) in days for a varying number of people ($$p$$) to dig a hole. How long would it take 3 people?

Q6.This graph shows the relationship between people and time required to build a wall. The point marked shows that 10 people would take 3 days. It would take 3 people days to build the wall.

Lesson appears in

UnitMaths / Linear graphs

Maths

Q1.
If it takes 2 hours to walk 6 miles, 3 hours to walk 9 miles, and 4 hours to walk 12 miles then the variables time and distance are said to ...

Q2.
Which of these graphs shows a directly proportional relationship?

Q3.
This time distance graph shows the relationship between the hours walked and the distance travelled in miles. What do the coordinates (5, 20) show?

Q4.
What is the equation of the line in this distance-time graph? Use $$d$$ for distance travelled and $$t$$ for time taken.

Q5.
For the equation $$s={30\over{t}}$$, when $$t=7.5$$, $$s=$$ .

Q6.
For the equation $$s={30\over{t}}$$, when $$s=7.5$$, $$t=$$

Q1.
When two variables are indirectly proportional, as one variable increases the other ...

Q2.
Inversely proportional relationships are modelled by the relationship ...

Q3.
Which of these graphs shows a relationship of indirect proportion?

Q4.
Why can this not be a graph of indirect proportion?

Q5.
This graph plots the time taken ($$t$$) in days for a varying number of people ($$p$$) to dig a hole. How long would it take 3 people?

Q6.
This graph shows the relationship between people and time required to build a wall. The point marked shows that 10 people would take 3 days. It would take 3 people days to build the wall.