The expression for equation of a straight line is given as
[tex]\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}[/tex]
An expression for m, the slope is given as
[tex]\begin{gathered} m\text{ =}\frac{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}[/tex]
Therefore, the slope is given as
[tex]\begin{gathered} m\text{ =}\frac{900-450}{10-4} \\ m\text{ =}\frac{450}{6}=75 \end{gathered}[/tex]
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
