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This topic covers direct proportion (y = kx) and inverse proportion (y = k/x), finding the constant k and using it to solve problems and interpret the graphs. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
For direct proportion write y equals kx; for inverse write y equals k over x. Substitute the pair of values you are given to find k, then use the formula with k in place for the value you need.
Before you start
Check ratio and substitution first if this feels hard. It is Foundation and Higher tier material at GCSE and iGCSE. It reappears throughout proportion graphs and formulae. It is part of the Ratio & Proportion strand.
What you learn
Two quantities are in proportion when they are linked by a fixed constant k. In direct proportion the equation is y = kx; in inverse proportion it is y = k⁄x. When y is directly proportional to x (written y ∝ x), the equation is y = kx, where k is the constant of proportionality. When y is inversely proportional to x (written y ∝ 1⁄x), the equation is y = k⁄x. The course works through direct proportion: y = kx, inverse proportion: y = k⁄x and recognising and using proportion. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Direct & Inverse Proportion is part of the Ratio and Proportion strand of our free GCSE maths courses, studied in Foundation tier. It runs to 3 concepts, each followed by a check, with 2 worked examples along the way. Related topics students usually take next include Exchange Rates & Best Value, Growth & Decay, Percentage Change and Proportion Graphs. You can drill this strand further on the Ratio and Proportion revision engine, with your accuracy saved to your skill tree.
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