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Direct
Model: y=kx; y/x constant; graph passes through origin
Unit rate: 5 notebooks £12.50 → each £2.50 → eight £20
Inverse
Model: y=k/x; xy constant; positive doubling x halves y
Assumptions: Fixed job/distance and unchanged rate needed
Use / evaluate
Constant: Find k from known pair, then substitute new input
Context: Fixed fee, changing total or productivity may break model
Powers
Specified relation: Higher: y=kx² or k/x²; doubling effects differ
Root / graph: Higher: y=5√x; plot y against x² for y=kx² to read k
Connections
Direct → Inverse: Ratios or products identify the proportional model
Use / evaluate → Powers: Known pairs determine the model constant
