Variation
Direct variation
A relationship where one quantity increases as the other increases, written y = kx.
| English | Direct variation |
|---|---|
| Bahasa Melayu | Variasi langsung |
| 中文 | 正变 |
How it is used
If y varies directly as x and y = 15 when x = 5, then k = 15 ÷ 5 = 3, so y = 3x. When x = 8, y = 3 × 8 = 24.
Where it shows up in SPM
Direct variation opens the Form 5 Variation chapter. In Paper 1 it is a short question finding k or a missing value; in Paper 2 it appears in word problems where one quantity, such as wages, varies directly with hours worked.
Don't confuse it with
Frequently asked questions
How do I find k in direct variation?
Substitute a matching pair of values into y = kx and divide. If y = 15 when x = 5, then k = y ÷ x = 15 ÷ 5 = 3.
Once you have k = 3, the rule y = 3x works for every other pair in the question.
Does the graph of y = kx always pass through the origin?
Yes. When x = 0, y = k × 0 = 0, so the line always goes through (0, 0).
This is how you tell direct variation from a general straight line, which can cross the y-axis at another point.
Can y vary directly with x² or √x?
Yes. SPM includes y = kx², y = kx³ and y = k√x.
The method is the same: find k from one pair, then use the rule. For y = kx² with y = 18 when x = 3, k = 18 ÷ 9 = 2, so y = 2x².