Problem

For $C(h)=25h+40$, interpret the slope as a repair-cost rate with units, state its $\text{one}\text{-}\text{hour}$ meaning and the change over $3~\text{hours}$, and distinguish it from the intercept.

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What this problem is really about

A slope interpretation must name its sign, its rate, and its output-per-input units. We’ll connect the variable coefficient to the cost change for one additional hour, then scale that rate over several hours. Keeping the constant term separate will prevent the one-time initial charge from being mistaken for the hourly rate.

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slope = +25 dollars/hour; one-hour meaning = each hour adds $25; 3-hour change = +$25 total; intercept distinction = $40 is the initial fee

slope = +40 dollars/hour; one-hour meaning = each hour adds $40; 3-hour change = +$120; intercept distinction = $25 is the initial service fee

slope = +25 dollars/hour; one-hour meaning = each additional repair hour adds $25; 3-hour change = +$75; intercept distinction = $40 is the initial service fee, not the hourly rate

slope = +25 hours/dollar; one-hour meaning = each extra dollar adds 25 hours; 3-hour change = +$75; intercept distinction = $40 is the initial fee

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For \(C(h)=25h+40\), interpret the slope as a repair-cost rate with units, state its \(\text{one}\text{-}\text{hour}\) meaning and the change over \(3~\text{hours}\), and distinguish it from the intercept.

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