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 y - intercept

The line crosses the y - axis at the point $(0,100)$. So the y - intercept $b = 100$. This represents the set fee for the house call.

Step2: Find two points on the line

Two points on the line are $(0,100)$ and $(5,450)$.

Step3: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,100)$ and $(x_2,y_2)=(5,450)$. Then $m=\frac{450 - 100}{5-0}=\frac{350}{5}=70$.

Step4: Write the equation of the line

The slope - intercept form of a line is $C=mt + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 70$ and $b = 100$, we get $C = 70t+100$.

Answer:

The equation for $C$ is $C = 70t + 100$. The slope of the graph is $70$. In the context of the problem, the slope represents the hourly rate that the electrician charges, which is $\$70$ per hour.