This topic summary covers Knowledge Organiser: Direct Proportion within Direct Proportion for GCSE Mathematics. Revise Direct Proportion in Ratio & Proportion for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 9 of 9 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Direct Proportion
Key Terms
- Direct proportion: When two quantities increase or decrease together at the same rate
- y ∝ x: Symbol meaning "y is directly proportional to x"
- Constant of proportionality (k): The fixed multiplier connecting y and x
- Unitary method: Finding the value for 1 unit first, then scaling up
Must-Know Facts
- y ∝ x means y = kx, where k is constant
- k = y ÷ x (the ratio of y to x is always the same)
- Graph of y against x is a straight line THROUGH the origin (0, 0)
- When x doubles, y doubles; when x triples, y triples
- Higher tier: y ∝ x² means y = kx² (graph is a curve, not a line)
Key Formulas
- y = kx (direct proportion equation)
- k = y ÷ x (find the constant from a pair of values)
- Higher: y = kx² or y = k√x
- Unitary: find value for 1 unit first, then multiply
Common Mistakes
- Not finding k first: Must substitute a known pair to find k before using the equation
- y = kx vs y = x + k: Direct proportion means proportional (through origin), not just linear
- y ∝ x² vs y ∝ x: Different equations — y ∝ x² means y = kx², not y = kx
- Graph shape: y = kx is a straight line through the origin; y = kx² is a curve
Practice questions for Direct Proportion
Which of the following correctly reads the mathematical statement y ∝ x?
Explain what it means for y to be directly proportional to x. Your answer should refer to the equation and the graph.
Quick recall flashcards
What does the symbol ∝ mean?
'is proportional to'
y ∝ x means 'y is proportional to x'
This is equivalent to writing y = kx for some constant k.
What does the graph of y = kx look like?
A straight line passing through the origin (0, 0).
The gradient of the line equals k.
If the line does NOT pass through (0,0), it is NOT direct proportion.