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 CC represent the total cost of the visit when the electrician spends tt hours at the house working. The table below has select values showing the linear relationship between tt and C.C. Determine the hourly rate charged.

Answer 1

We need to obtain the equation of the line in order to determine the initial charge

we have

(4.5,12.75)=(x1,y1)

(9,19.50)=(x2,y2)

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{19.50-12.75}{9-4.5}=1.5$

then we have

$C-C_1=m(t-t_1)$

in this case

C1=12.75

t1=4.5

$\begin{gathered} C-12.75=1.5(t-4.5) \\ C=1.5t-6.75+12.75 \\ C=1.5t+6 \end{gathered}$

As we can see the initial fee is 6