Determine whether a relationship is proportional from a table, graph, equation, or context.
Choose a smart proportionality test
Problem
A table has \(x~=~2,5,8,11\) and \(y~=~7,17.5,28,38.5\). Consider these tests: A, compare \(y/x\); B, compare \(y\) differences; C, require an \(x=0\) row; D, claim the ratios differ. Choose the test that works, then classify the relationship.
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What this problem is really about
Because the representation is a table, the decisive question is whether one multiplier carries every x-value to its paired y-value. We’ll evaluate the proposed tests by calculating y divided by x for all four rows, then express any common quotient as a rule of the form y equals kx. Differences or a missing zero row are not the direct test.
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