Question

an electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. the total cost of the electricians services can be determined using the equation $c = 65 + 60t$, where $t$ is the number of hours the electrician spends at the house working. what is the slope of the equation and what is its interpretation in the context of the problem?

answer attempt 1 out of 2

the slope of the function is \boxed{} which represents

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(C=65 + 60t\), we can rewrite it in the form \(C = 60t+65\), which is similar to \(y=mx + b\) with \(y = C\), \(x = t\), \(m = 60\) and \(b = 65\).

Step2: Interpret the slope in context

In the context of the problem, \(C\) is the total cost and \(t\) is the number of hours. The slope (the coefficient of \(t\)) represents the rate of change of the total cost with respect to the number of hours. So, the slope of 60 means that for each additional hour the electrician works (\(t\) increases by 1), the total cost \(C\) increases by 60 dollars. So the slope represents the electrician's hourly rate.

Answer:

The slope of the function is \(60\) which represents the electrician's hourly rate (the amount the total cost increases for each additional hour of work).