Proportion modelling
Objective. Choose and critique proportional models from data.
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- 2. Worked example
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Learn: the key idea
Proportion modelling involves choosing between direct and inverse proportional models based on real data, then testing and critiquing how well the model fits. To decide if data is directly proportional, check whether y/x stays constant across all pairs; for inverse proportion, check whether xy stays constant instead. If neither ratio is constant, the relationship may not be a simple proportion, and you should state this rather than forcing a model. For example, data pairs (2,10), (4,20), (6,30) all give y/x=5, confirming direct proportion with k=5. Always test multiple data pairs before concluding which model, if any, fits the data.
Worked example
Data pairs (x,y) are (2, 24), (3, 16), (4, 12). Determine whether this data shows inverse proportion and state k.
- 1Test xy for each pair: 2×24=48
- 2Check next pair: 3×16=48
- 3Check third pair: 4×12=48
- 4Since xy is constant at 48, the data shows inverse proportion with k=48
Answer: Inverse proportion, k = 48
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Practice
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Start practisingCommon mistake. Pupils assume any data showing increase must be direct proportion without checking that y/x is actually constant. For pairs (1,3), (2,5), (3,9), the ratios 3, 2.5, 3 are not constant, so it is not direct proportion despite increasing values. Always verify the constant ratio or product before naming the model.
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