Question

an electrician charges a set field for every house call and then charges an hourly rate depending on how long the job take let C represent the total cost of the visit when the electrician spent T hours at the house working. A graph of C is shown below. Write an equation for C then State the slope of the graph and determine its interpretation in the context of the problem

Answer 1

The expression for equation of a straight line is given as

`\begin{gathered} y\text{ = mx + c} \\ \text{Modeling from the question, the required equation is} \\ C\text{ = mT + c} \\ \text{where} \\ C\text{ = Total cost of the visit or for all services} \\ T\text{ = hours spent at the hours working} \\ m\text{ = slope} \\ c\text{ = y-intercept} \end{gathered}`

An expression for m, the slope is given as

`\begin{gathered} m\text{ =}(y_2-y_1)/(x_2-x_1) \\ \text{Where, from the graph} \\ y_2=\text{ 900} \\ y_1=450 \\ x_2=10 \\ x_1=4 \end{gathered}`

Therefore, the slope is given as

`\begin{gathered} m\text{ =}(900-450)/(10-4) \\ m\text{ =}(450)/(6)=75 \end{gathered}`

The slope = 75

The slope represents the hourly rate charged

The equation for C , is C = 75t + c

From the graph c = 150

Therefore, the required final equation for C is

C = 75T + 150

C represents the total cost of all services the electrician provided

In 1 hours, his total cost will be

C = 75(1) + 150

C = $225