Inverse proportion graphs
The Maths Habit Handout to print
The more people help,
the quicker a job gets done.
Is that always true?
Painting a fence: yes, up to a point
Watching a film: no
Boiling a kettle: no, it takes the same time
What is x × y every time?
| x | 1 | 2 | 4 |
|---|---|---|---|
| y | 20 | 10 | 5 |
It takes 2 people 12 hours to build a fence.
| People | 1 | 2 | 3 | 4 | 6 |
|---|---|---|---|---|---|
| Hours | 12 |
A curve that never touches the axes
A journey takes 3 hours at 20 mph. Draw the graph. Find the time at 40 mph.
| Speed (mph) | Time (hours) |
|---|---|
| 10 | 6 |
| 20 | 3 |
| 30 | 2 |
| 50 | 1.2 |
| 60 | 1 |
4 taps fill a pool in 6 hours. Draw the graph. Find the time for 8 taps.
| Taps | Hours |
|---|---|
| 1 | 24 |
| 2 | 12 |
| 3 | 8 |
| 4 | 6 |
| 6 | 4 |
| 12 | 2 |
A journey takes 3 hours at 20 mph. Draw the graph. Find the time at 40 mph.
| Speed (mph) | Time (hours) |
|---|---|
| 10 | 6 |
| 20 | 3 |
| 30 | 2 |
| 50 | 1.2 |
| 60 | 1 |
3 machines take 10 hours. Draw the graph. Find the time for 5 machines.
| Machines | Hours |
|---|---|
| 1 | 30 |
| 2 | 15 |
| 3 | 10 |
| 6 | 5 |
| 10 | 3 |
A journey takes 3 hours at 20 mph. Draw the graph. Find the time at 40 mph.
| Speed (mph) | Time (hours) |
|---|---|
| 10 | 6 |
| 20 | 3 |
| 30 | 2 |
| 50 | 1.2 |
| 60 | 1 |
2 diggers take 9 days to dig a trench. Draw the graph. Find the time for 3 diggers.
| Diggers | Days |
|---|---|
| 1 | 18 |
| 2 | 9 |
| 4 | 4.5 |
| 6 | 3 |
| 9 | 2 |
A journey takes 3 hours at 20 mph. Draw the graph. Find the time at 40 mph.
| Speed (mph) | Time (hours) |
|---|---|
| 10 | 6 |
| 20 | 3 |
| 30 | 2 |
| 50 | 1.2 |
| 60 | 1 |
A trip takes 3 hours at 40 mph. Draw the graph. Find the speed for a 2 hour trip.
| Speed (mph) | Time (hours) |
|---|---|
| 20 | 6 |
| 30 | 4 |
| 40 | 3 |
| 80 | 1.5 |
| 100 | 1.2 |
A journey takes 3 hours at 20 mph. Draw the graph. Find the time at 40 mph.
| Speed (mph) | Time (hours) |
|---|---|
| 10 | 6 |
| 20 | 3 |
| 30 | 2 |
| 50 | 1.2 |
| 60 | 1 |
A prize gives 4 winners £15 each. Draw the graph. Find each share for 5 winners.
| Winners | Share (£) |
|---|---|
| 1 | 60 |
| 2 | 30 |
| 3 | 20 |
| 4 | 15 |
| 6 | 10 |
Answer sheet
An inverse proportion curve goes through (4, 6). Does it also go through (3, 8)? How do you know?
Yes8 pumps empty a tank in 3 hours. How many pumps would empty it in 2 hours?
12 pumpsA straight line goes through (2, 6) and (3, 4). For both points, x × y = 12. Can the line show inverse proportion? Explain.
No: it also goes through (4, 2), and 4 × 2 = 8, not 12
x and y are inversely proportional.
Complete the table.8 and 6x 2 4 6 8 y 24 12 Which graph shows inverse proportion?
BAn inverse proportion curve goes through (4, 9). Does it go through (6, 5)? Explain.
No: 6 × 5 = 30, not 36