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 $c$ represent the total cost of the 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 slope of the graph and determine its interpretation in the context of the problem.

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is $C=mt + b$, where $m$ is the slope and $b$ is the $y$ - intercept.

Step2: Find the $y$ - intercept

The line crosses the $C$ - axis at $(0,100)$, so $b = 100$.

Step3: Calculate the slope

Using two points $(0,100)$ and $(2,250)$, slope $m=\frac{250 - 100}{2-0}=\frac{150}{2}=75$.

Step4: Write the equation

Substitute $m = 75$ and $b = 100$ into $C=mt + b$ to get $C = 75t+100$.

Step5: Interpret the slope

The slope represents the rate of change of the cost with respect to time. So the electrician charges $75$ dollars per hour.

Answer:

Equation: $C = 75t+100$; Slope: $75$; Interpretation: The electrician's hourly rate is $75$ dollars per hour.