Evaluate each representation for proportionality. Report the letter of the proportional representation.
A. A table with \(x\text{-}\text{values}~2,~4,~6\) and \(y\text{-}\text{values}~10,~20,~30\)
B. An equation \(y~=~5x~+~2\)
C. A graph of a line that crosses the \(y\text{-}\text{axis}\) at \(3\)
D. A situation where a gym charges a \(\$12~\text{sign}\text{-}\text{up}~\text{fee}\) and \(\$4~\text{per}~\text{visit}\)
What this problem is really about
Each representation needs its own proportionality test. We’ll compare output-to-input ratios in the table, look for an added term in the equation, check whether the graph passes through the origin, and identify any fixed fee in the context. A constant rate is proportional only when there is also no nonzero starting amount.