Knowledge Organiser: Proportion Graphs
Part of Proportion · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Proportion Graphs within Proportion for GCSE Mathematics. Revise Proportion in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 16 of 16 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 16 of 16
Practice
12 questions
Recall
22 flashcards
Knowledge Organiser: Proportion Graphs
Key Terms
- Constant of proportionality (k): The fixed number linking y and x in any proportion equation
- Direct proportion (y = kx): Straight line through the origin
- y ∝ x²: y is proportional to x squared — a curved graph (parabola) through origin
- Inverse proportion (y = k/x): A hyperbola — curve that never touches the axes
- Origin: The point (0, 0) — all direct proportion graphs pass through here
Must-Know Facts
- y = kx → straight line through origin (gradient = k)
- y = kx² → curved graph through origin (parabola shape)
- y = k/x → hyperbola, never touching either axis
- Find k by substituting a given pair of x and y values into the equation
- If y doubles when x doubles: direct. If y halves when x doubles: inverse
- If y quadruples when x doubles: y ∝ x²
Key Formulas
- y = kx (direct proportion; k = y ÷ x)
- y = kx² (proportional to square; k = y ÷ x²)
- y = k/x (inverse; k = x × y)
- y = k√x (proportional to square root; k = y ÷ √x)
Common Mistakes
- Identifying graph type: Straight line through origin = direct; curve through origin = power/root; hyperbola = inverse
- y-intercept not zero: y = kx must pass through (0, 0) — if it doesn't, it is NOT direct proportion
- Confusing y = kx² with y = (kx)²: These give different graphs — the power applies only to x
- Finding k from graph: Read off a clear point (not the origin) and substitute into the correct equation
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Practice Questions for Proportion
y is directly proportional to x. Which equation could represent this relationship?
Explain how you can tell from a graph whether two quantities are in direct or inverse proportion.
Quick Recall Flashcards
12 questions on Proportion — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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