Question

An electrician charges a set fee for every house call and then charges an hourly ratedepending on how long the job takes. The total cost of the electrician's services can bedetermined using the equation C = 65 + 60t, where t is the number of hours theelectrician spends at the house working. What is the slope of the equation and what isits interpretation in the context of the problem?

Answer 1

We have the equation:

$C(t)=65+60t$

Given the slope-intercept formula for the equation of the line, we have the following:

$\begin{gathered} y=mx+b \\ m\colon\text{ slope} \\ If\text{ C=65+60t} \\ \Rightarrow slope\text{ = 60} \end{gathered}$

Now, since we have that t is the number of hours the electrician spends working, the slope of the function represents the hourly rate charged.