Distinguish proportional relationships from linear but non-proportional relationships.
Compare two linear forms for proportionality
Problem
Relationship \(A\) is given by \(y~=~2x\). Relationship \(B\) is given by \(y~=~2x~+~5\). For each relationship, decide whether it is proportional or linear but not proportional.
Big Picture
What this problem is really about
The two rules have the same rate, but equal slopes alone do not settle proportionality. Evaluate each rule at zero or inspect its constant term, because a proportional linear relationship must have zero starting value and pass through the origin. Classify each relationship independently from that test rather than transferring one label to both.
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