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

The linear model that represents the total cost as a function of the number of hours worked is y = 35x + 50. The electrician fee is $50, which is the y-intercept of the equation. The electrician charges $35 per hour.

Step-by-step explanation:

To write a linear model that represents the total cost as a function of the number of hours worked, we can use the given information to find the slope and y-intercept. Let's assign the number of hours worked as x and the total cost as y.

We have two data points: (2, 120) and (4, 190). Using these points, we can find the slope (m) and y-intercept (b) of the linear equation.

The formula for the slope is m = (y2 - y1) / (x2 - x1). Using (2, 120) and (4, 190), we have m = (190 - 120) / (4 - 2) = 70 / 2 = 35.

Next, we can use the point-slope form y - y1 = m(x - x1) with one of the data points and the slope to find the y-intercept. Let's use (2, 120). Substituting the values, we get y - 120 = 35(x - 2).

Simplifying the equation, we get y = 35x - 70 + 120 = 35x + 50.

So, the linear model that represents the total cost as a function of the number of hours worked is y = 35x + 50.

The electrician fee can be determined by looking at the y-intercept, which is 50 dollars. This represents the fixed cost or base fee charged by the electrician.

To find the electrician's charge per hour, we can look at the coefficient of the x term, which is 35 dollars. This represents the rate or cost per hour charged by the electrician.

Answer 2

`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=(y_2-y_1)/(x_2-x_1)`

`m=(190-120)/(4-2)`

`m=(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.