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. the total cost of the electrician’s services can be determined using the equation ( c = 110 + 55t ), where ( t ) is the number of hours the electrician spends at the house working. what is the slope of the equation and what is its interpretation in the context of the problem?
answer
attempt 1 out of 2
the slope of the function is (square) which represents (square).

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given equation $C=110 + 55t$, we can rewrite it in the form $C = 55t+110$, which is in the form of $y=mx + b$ (where $y = C$, $x = t$, $m = 55$ and $b = 110$).

Step2: Interpret the slope

In the context of the problem, $t$ represents the number of hours the electrician works and $C$ represents the total cost of the electrician's services. The slope $m = 55$ represents the rate of change of the total cost with respect to the number of hours worked. Since the electrician charges an hourly rate, the slope of $55$ means that the electrician's hourly rate is $55$ dollars per hour. For each additional hour the electrician works ($t$ increases by 1), the total cost $C$ increases by $55$ dollars.

Answer:

The slope of the function is $55$, which represents the electrician's hourly rate (the increase in the total cost of the electrician's services for each additional hour the electrician works).