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Direct and Inverse Proportion

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Proportion describes how two quantities change together. A unit rate is the amount for 1 unit, such as cost per apple or cartons per hour, and it often helps you spot the relationship.

In direct proportion, both quantities scale by the same factor, so if apples double, the cost doubles. The algebra model is y=kxy=kxy=kx, where kkk is the constant of proportionality.

In inverse proportion, increasing one quantity makes the other decrease by the same factor, so if workers double, the time halves. The algebra model is y=kxy=\frac{k}{x}y=xk​.

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Question 1

2 marks

A machine fills 1000 bottles in 5 hours.

Work out how many hours it would take the machine to fill 1200 bottles.

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What does a unit rate represent?

Direct and Inverse Proportion Revision Guide

  1. GCSE
  2. /Maths
  3. /Direct and Inverse Proportion

Revision notes for Edexcel GCSE Maths Direct and Inverse Proportion. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Writing a Ratio as a Fraction or Linear FunctionDirect and Inverse ProportionReverse PercentagesStandard FormSpeed and DensityChanging the Subject of a FormulaExpanding and Factorising QuadraticsSolving QuadraticsDrawing Quadratic GraphsDrawing Other Graphs: Cubic/ReciprocalSimultaneous EquationsSolving Simultaneous Equations GraphicallyMidpoint of a Line SegmentGradient of a LineEquation of a LineSpheres and ConesSector Areas and Arc LengthsSimilar Shapes (Lengths)SOHCAHTOA (Trigonometry)Exact trig valuesVectorsProbability TreesVenn Diagrams

Practise questions

1 of 5

A graph of yyy against xxx is a straight line through the origin and passes through the point (2,10)(2,10)(2,10). Which formula connects yyy and xxx?