Question

An electrician charges $120 after 2 hours of work and $190 after 4 hours of work.Write a linear model that represents the total cost as a function of the number of hours worked.What is the electrician fee. How much does the electrician charge per hour

Answer 1

Answer:

$C(x)=35x+50$

Electrician's fee: $50.

Charges per hour: $35

Step-by-step explanation:

Let x represent number of hours and y represent amount charged.

We have been given that an electrician charges $120 after 2 hours of work and $190 after 4 hours of work.

We can represent this information with two points as (2,120) and (4,190).

First of all, we will find slope using these points.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{190-120}{4-2}$  

$m=\frac{70}{2}$  

$m=35$  

Now, we will slope-intercept form of equation $y=mx+b$ to get our required equation as:

$y=35x+b$

Substitute coordinates of point (2,120) to find the y-intercept.

$120=35(2)+b$

$120=70+b$

$120-70=70-70+b$

$50=b$

Therefore, our required function would be $C(x)=35x+50$.

The electrician's fee would be $50 as it the initial amount or y-intercept.

The electrician charges $35 per hour as the slope of the line is 35.