Variation
Inverse variation
A relationship where one quantity decreases as the other increases, written y = k/x.
| English | Inverse variation |
|---|---|
| Bahasa Melayu | Variasi songsang |
| 中文 | 反变 |
How it is used
If y varies inversely as x and y = 4 when x = 6, then k = 4 × 6 = 24, so y = 24/x. When x = 3, y = 24 ÷ 3 = 8.
Where it shows up in SPM
Inverse variation follows direct variation in the Form 5 Variation chapter. Paper 1 asks you to find k or a value; Paper 2 sets word problems such as the number of workers and the time to finish a job.
Don't confuse it with
Frequently asked questions
How do I find k in inverse variation?
Multiply a matching pair of values, because xy = k. If y = 4 when x = 6, then k = 4 × 6 = 24, giving y = 24/x.
Do not divide, dividing is the method for direct variation, not inverse.
Why does the graph curve instead of being a straight line?
Because y = k/x is not linear. As x grows, y shrinks toward zero but never reaches it, giving a smooth curve in the first quadrant for positive k.
The curve never touches either axis.
What stays constant in inverse variation?
The product of the two quantities. If 6 workers take 4 days, that is 24 worker-days; 8 workers take 24 ÷ 8 = 3 days.
The 24 is k, and it stays fixed however the two quantities change.