If y is directly proportional to x², write y = kx². Use one pair of values to find k, then use the formula. When x = 8, y = 512, so 512 = 64k and k = 8, giving y = 8x².
If y is inversely proportional to x, write y = k/x: as one goes up, the other goes down. Proportion questions with powers have shortcuts: if y ∝ x³ and x doubles, then y is multiplied by 2³ = 8.
Worked example
y is directly proportional to √x. When x = 81, y = 45. Find y when x = 16.
- y = k√x: 45 = 9k, so k = 5.
- y = 5 × √16 = 20.
Answer:y = 20
Key words
- ∝
- is proportional to
- constant of proportionality (k)
- the fixed multiplier
- inverse proportion
- y = k/x
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