IGCSE Maths Direct & Inverse Proportion Notes
In direct proportion two quantities rise together; in inverse proportion one rises as the other falls. Both are modelled with a constant k.
Key concepts
- Direct proportion
- y ∝ x means y = kx; the graph is a straight line through the origin.
- Inverse proportion
- y ∝ 1/x means y = k/x; the graph is a reciprocal curve.
- Powers
- Relationships may involve x², √x, etc., e.g. y = kx².
Key formulas
Direct
y = kx
Inverse
y = k/x
Worked example
y is inversely proportional to x. y = 4 when x = 3. Find y when x = 6.
- 1Write y = k/x and find k: 4 = k/3, so k = 12.
- 2Use y = 12/x with x = 6.
- 3Calculate y.
Answer: y = 2
Common mistakes
✗ Using y = kx for an inverse relationship.
✓ Inverse proportion uses y = k/x.
✗ Not finding k before answering.
✓ Always calculate the constant from the given pair first.
✗ Ignoring a power in the relationship.
✓ Read whether it is proportional to x, x² or √x.
Quick check
Try these, then reveal the answers.
If y = kx and y = 15 when x = 3, find k.Reveal answer
5
y = k/x, k = 20. Find y when x = 4.Reveal answer
5
Direct-proportion graph shape?Reveal answer
Straight line through the origin
Exam tips
- Translate the proportion statement into an equation first.
- Find k using the given values before answering the question.
- Check the answer direction — inverse means larger x gives smaller y.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
How do I know if it is direct or inverse proportion?+
If both quantities increase together it is direct (y = kx); if one increases as the other decreases it is inverse (y = k/x).
What does the symbol ∝ mean?+
It means 'is proportional to' — you convert it to an equation by introducing the constant k.
Create a free account to practise direct & inverse proportion with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.