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Ratio & Proportion · Foundation & Higher

Direct proportion

Two quantities are in direct proportion if they increase and decrease at the same rate. When one doubles, the other doubles.

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Key facts to remember

  • 1If y is directly proportional to x: y = kx, where k is the constant of proportionality.
  • 2The graph of direct proportion is a straight line through the origin.
  • 3You can use the unitary method: find the value for 1, then multiply.
  • 4If y ∝ x², then y = kx² (direct proportion to the square).
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Formulas

Direct proportion
y = kx

k is constant

Find k
k = y/x (use a known pair)
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Worked examples

Example 1

y is directly proportional to x. When x = 4, y = 20. Find y when x = 7.

Working

  1. y = kx → 20 = k × 4 → k = 5
  2. y = 5x
  3. When x = 7: y = 5 × 7 = 35
Answery = 35
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Common mistakes

✗Not finding k first — always establish the formula before finding new values.
✗Confusing direct proportion (y = kx) with inverse proportion (y = k/x).
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Exam tips

✓Look for the words "proportional to" — they tell you the relationship type.
✓Find k using the given values, then use the formula for the unknown.

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