The target rate is \(+3~\text{in}~y~\text{for}~\text{each}~+1~\text{in}~x\). Which representations have the same unit rate as the target?
A. Bike rental cost increases \(\$9~\text{over}~3~\text{hours}\).
B. Points \((1,~4)\) and \((3,~10)\).
C. A table has \(x\text{-}\text{values}~0,~2,~4\) and \(y\text{-}\text{values}~5,~11,~17\).
D. A graph movement goes \(\text{right}~4~\text{and}~\text{up}~12\).
E. A table has \(x\text{-}\text{values}~2,~3,~4\) and \(y\text{-}\text{values}~7,~10,~13\).
F. Points \((2,~9)\) and \((5,~18)\).
What this problem is really about
Representations with different-looking changes can still describe the same rate, so reduce each one to output change per one input unit. Use matching intervals and consistent subtraction order for contexts, point pairs, tables, and graph movement, then compare the normalized values with the target. This tests equivalence instead of requiring the raw changes to look identical.