Distinguish proportional relationships from linear but non-proportional relationships.
Convert without changing proportionality
Problem
A table maps \(x\text{-}\text{values}~0,~2,~4,~6\) to \(y\text{-}\text{values}~3,~7,~11,~15\). Write its equation and classify the relationship as proportional or non-proportional.
The table’s raw output change is not automatically the coefficient when the input jumps by more than one. Compute the unit rate as output change divided by input change, read the zero-input row for the constant term, and combine them into a linear rule. Finally, use that zero-input value to determine whether the rule is proportional.
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