Variation
Direct variation
A relationship where one quantity increases at a constant rate as another increases, y = kx.
| English | Direct variation |
|---|---|
| Bahasa Melayu | Variasi langsung |
| 中文 | 正比 |
How it is used
If 3 exercise books cost RM6, the cost is directly proportional to the number of books, so k = 6 ÷ 3 = RM2 each. Then 7 books cost 7 × 2 = RM14.
Where it shows up in SPM
Direct proportion is the everyday wording of direct variation, used across the Form 5 Variation chapter. It shows up in both papers as real-life word problems on cost, currency exchange and recipe scaling, where you find the rate then scale up or down.
Don't confuse it with
Frequently asked questions
What is the difference between direct proportion and direct variation?
They describe the same relationship, y = kx. 'Proportion' stresses that the ratio y/x is constant, while 'variation' stresses the equation.
In SPM you may see either wording, and the working is identical.
How do I check if two quantities are directly proportional?
Divide each y by its matching x. If the ratio is the same every time, they are directly proportional.
For 3 books at RM6 and 7 books at RM14, both give 2, so cost is proportional to the number of books.
If x doubles, what happens to y?
In direct proportion, y also doubles. Because y = kx, replacing x with 2x gives 2kx = 2y.
This 'double one, double the other' test is a quick way to recognise a directly proportional situation.