Question

An electrician charges a set fee for every house call and then charges an hourly ratedepending on how long the job takes. Let C represent the total cost of the visit whenthe electrician spends t hours at the house working. The table below has select valuesshowing the linear relationship between t and C. Determine the set fee for the housecall.t C2 2505 4306.5 520

Answer 1

Start by finding the slope, which will be the hourly rate the electrician charges using the formula

`m=(y_2-y_1)/(x_2-x_1)`

use points (2,250) and (5,430)

replace in the formula

`\begin{gathered} m=(430-250)/(5-2) \\ m=(180)/(3) \\ m=60 \end{gathered}`

now, use of the points to find the set fee using

`\begin{gathered} C=mt+b \\ C=60t+b \end{gathered}`

use point (6.5,520)

`\begin{gathered} 520=60\cdot(6.5)+b \\ 520-390=b \\ 130=b \end{gathered}`

The set fee is $130