Determine whether a relationship is proportional from a table, graph, equation, or context.
Judge proportionality in context
Problem
Tickets cost \(\$4~\text{each}\): \((1,\$4)\), \((3,\$12)\), and \((6,\$24)\), with \(\text{no}~\text{fee}\). Classify the relationship and state its determining feature: constant unit rate with \(\text{zero}~\text{start}\) or \(\text{nonzero}~\text{starting}~\text{fee}\).
Big Picture
What this problem is really about
The determining evidence is whether every ticket-cost pair shares one cost per ticket and whether the relationship starts at zero. We’ll divide each cost by its matching ticket count, write the resulting cost rule, and evaluate that rule at zero tickets. Unequal gaps between the listed inputs do not affect this constant-ratio test.
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