Recognize constant rate of change as evidence for a linear model.
Correct a linear model with swapped rate and initial value
Problem
Write the linear equation for a situation that starts at \(12\) and increases by \(5~\text{each}~\text{week}\).
Big Picture
What this problem is really about
A quick zero-input test exposes which number is the initial value in a linear model. We’ll pair the standalone constant with the starting amount and the input coefficient with the weekly change, then rebuild the rule in those roles. Checking weeks zero and one will confirm both the start and the one-step increase.
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