Inverse Proportion
Use y = k/x when one quantity falls as the other rises, find k from a given pair, and recognise the curve it produces.
What a learner can do afterwards
- Tell direct from inverse proportion in a word problem
- Find k and use it, for example with workers and the time a job takes
- Describe the shape of an inverse proportion graph
1 · Read
Direct proportion grows together, while inverse proportion trades off. More taps fill the tank faster, and more workers finish the job sooner. When one quantity doubles while the other halves, the product stays fixed, and that fixed product is the signature of inverse proportion.
Four taps fill a tank in 6 hours. Double the taps to 8 and the time halves to 3 hours. The job itself never changes: 5 workers for 8 days is 40 worker-days, and 4 workers need 40 divided by 4, which is 10 days. Find the fixed total first, then divide.
The constant k pins the rule down through y equals k over x. With x equal to 3 and y equal to 10, multiply to find k equal to 30. Every other pair must multiply to 30 as well, so y is 6 when x is 5. One pair buys the whole rule.
Graphs tell the two apart at a glance. Direct proportion draws a straight line through the origin, while inverse proportion draws a curve that falls steeply near zero then flattens, never touching either axis. In words, splitting money by ratio grows together, while sharing a fixed job trades off.
Spot the trade-off, find the fixed product, then divide.
2 · Watch
Take it off screen
Where it sits
Learn first
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.