Distinguish proportional relationships from linear but non-proportional relationships.
Decide whether a story is proportional
Problem
A bike rental costs \(\$3~\text{per}~\text{hour}\) with \(\text{no}~\text{starting}~\text{fee}\). Determine the cost at \(0~\text{hours}\) and classify the relationship as proportional or linear but not proportional.
Big Picture
What this problem is really about
Translate the story into total cost equals hourly rate times hours plus any starting fee. Evaluate that model at zero hours, then check whether every nonzero cost-to-hours ratio stays equal to the stated unit rate. Proportionality requires both constant scaling and no amount already present before any hours are used.
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