Identify \(\text{every}~\text{representation}\) equivalent to \(y~=~3x~+~2\).
A. A table with \(x\text{-}\text{values}~0,~1,~2,~3~\text{and}~y\text{-}\text{values}~2,~5,~8,~11\)
B. The rule: \(\text{start}~\text{at}~3~\text{and}~\text{add}~2~\text{for}~\text{each}~1~\text{increase}~\text{in}~x\)
C. The points \((1,~5),~(2,~8),~(4,~14)\)
D. A table with \(x\text{-}\text{values}~0,~1,~2,~3~\text{and}~y\text{-}\text{values}~3,~5,~7,~9\)
E. The equation \(y~=~2x~+~3\)
F. The description: the output is \(2~\text{more}~\text{than}~3~\text{times}~\text{the}~\text{input}\)
What this problem is really about
Use the target equation as a two-feature fingerprint: its zero-input value and its output change per one input unit. Translate every table, point set, rule, and verbal statement into that common description or test shared inputs directly. A representation must preserve both features; merely containing the same two numbers in reversed roles is not enough.