Distinguish proportional relationships from linear but non-proportional relationships.
Match a story to the right kind of linear form
Problem
Model a delivery company's \(\$4\) starting charge plus \(\$2~\text{per}~\text{mile}\) \(x\) with an equation. A. \(y~=~2x\) B. \(y~=~2x~+~4\) C. \(y~=~4x~+~2\) D. \(y~=~x~+~4\)
Big Picture
What this problem is really about
Separate the delivery cost into the amount charged before any miles and the amount repeated for each mile. The first becomes the equation’s constant term, while the per-mile rate multiplies the mileage variable; a zero-mile and one-mile check confirms their roles. This prevents the two given numbers from being swapped or one of them omitted.
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