Distinguish proportional relationships from linear but non-proportional relationships.
Model a story, then test proportionality
Problem
A candle starts at \(12~\text{centimeters}\) and loses \(2~\text{centimeters}~\text{per}~\text{hour}\). Build the height table for hours \(0~\text{through}~4\) and classify the relationship as proportional or non-proportional.
Big Picture
What this problem is really about
Build the table from a model, not from a guessed pattern: height equals the initial height plus the signed hourly change times elapsed time. Evaluate that rule at every requested hour, including hour zero, and check the repeated difference. Then use the zero-hour row to distinguish a proportional relationship from a merely linear one.
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