Question

an electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. let c rep visit when the electrician spends t hours at the house working. a graph of c is shown below. write an equation for c then state the determine its interpretation in the context of the problem. answer attempt 1 out of 2 c = the slope of the function is which represents the set fee for the house call the number of hours the electrician spends at the house the hourly rate charged the total cost for all services the number of hours the electrician spends at the house

Explanation:

Step1: Find the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((0,150)\) and \((2,300)\).
\(m=\frac{300 - 150}{2-0}=\frac{150}{2}=75\)

Step2: Write the equation

The equation of a line in slope - intercept form is \(C = mt + b\), where \(b\) is the \(y\) - intercept. From the graph, when \(t = 0\), \(C=150\) (so \(b = 150\)) and \(m = 75\).
So the equation is \(C=75t + 150\)

Answer:

\(C = 75t+150\); The slope of the function is \(75\) which represents the hourly rate charged.