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
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.
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