Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Construct a linear function from a context
Problem
Construct the linear function for a plumber who charges \(45~\text{dollars}\) to visit plus \(30~\text{dollars}~\text{per}~\text{hour}\).
Big Picture
What this problem is really about
A contextual linear model separates the charge that repeats with the input from the charge paid only once. We’ll identify hours as the input, attach the hourly units to the variable term, and treat the visit fee as the zero-hour starting value. Checking both zero hours and one additional hour will confirm the model’s structure.
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