Recognize constant rate of change as evidence for a linear model.
Judge whether a context should be modeled linearly
Problem
Decide whether this situation should be modeled with a linear function: A worker earns \(16~\text{dollars}~\text{for}~\text{each}~\text{hour}~\text{worked}\) plus no bonus.
Big Picture
What this problem is really about
Whether a context is linear depends on constant change, not on whether the formula contains multiplication or a bonus. We’ll identify the amount added for each equal input step and the output present at zero input, then express those roles in a model. Testing consecutive inputs will show whether one rate applies throughout.
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