Find and interpret the constant of proportionality in multiple representations.
Check a proposed contextual constant
Problem
With \(x~=~\text{gallons}\) and \(y~=~\text{miles}\), a car travels \(48~\text{miles}\) on \(12~\text{gallons}\). Jada claims \(k~=~4~\text{miles}~\text{per}~\text{gallon}\). Classify the claim and give corrected \(k\) with units.
Big Picture
What this problem is really about
Since x is gallons and y is miles, the proposed k must be checked as miles divided by gallons. We’ll calculate that output-to-input quotient from the trip, compare both its number and units with the claim, and multiply the resulting rate by twelve gallons. Reconstructing forty-eight miles provides an independent verification.
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