EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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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.

Revising direct proportion the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Direct proportion GCSE” on the site for the complete guide.

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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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