Question

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.
answer attempt 1 out of 2
$c = square$
the slope of the function is $square$ which represents

Explanation:

Step1: Find the y - intercept

The graph intersects the $C$ - axis at $(0,100)$. So the set - fee (when $t = 0$) is $100$.

Step2: Find two points on the line

Let's take two points $(0,100)$ and $(10,800)$.

Step3: Calculate the slope

The slope formula is $m=\frac{C_2 - C_1}{t_2 - t_1}$. Substituting $(t_1,C_1)=(0,100)$ and $(t_2,C_2)=(10,800)$ gives $m=\frac{800 - 100}{10-0}=\frac{700}{10}=70$.

Step4: Write the equation of the line

The equation of a line in slope - intercept form is $C=mt + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 70$ and $b = 100$ gives $C = 70t+100$. The slope $70$ represents the amount the total cost increases for each additional hour of work, i.e., the hourly rate the electrician charges.

Answer:

$C = 70t+100$; The slope of the function is $70$ which represents the hourly rate the electrician charges.