This topic summary covers Knowledge Organiser: Proportion Graphs within Proportion Graphs for GCSE Mathematics. Revise Proportion Graphs in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 4 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and 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
Practice questions for Proportion Graphs
Which of the following describes the graph of a direct proportion relationship?
Aisha says: 'Because the graph of y against x is a straight line, y must be directly proportional to x.' Is Aisha correct? Explain your answer.
Quick recall flashcards
Direct vs Inverse
Direct: both increase together (y ∝ x). Inverse: one increases, other decreases (y ∝ 1/x).
Finding k
Use given values to find constant k, then apply to new values