Question

select all the correct statements.

the amount in dollars an electrician charges in terms of the number of hours worked is represented by the function \\(y = 22x + 42\\).

from the function, identify all the phrases that hold true for the situation.

• the electrician charges an initial fee of \\$22.
• the \\(y\\)-variable represents the number of hours.
• the electrician charges an initial fee of \\$42.
• the electrician charges \\$22 for every hour worked.
• the \\(x\\)-variable represents the electricians charges in dollars.
• the electrician charges \\$42 for every hour worked.

Explanation:

Identify variables and function

We are given the linear function \(y = 22x + 42\).

• \(y\) represents the total amount charged in dollars.
• \(x\) represents the number of hours worked.

Analyze the slope

Using the Linear Equations concept, we identify the slope \(m = 22\).

• The slope represents the rate of change.
• Here, it means the electrician charges \$22 for every hour worked.

Analyze the y-intercept

Using the Linear Equations concept, we identify the y-intercept \(b = 42\).

• The y-intercept represents the initial value when \(x = 0\).
• Here, it means the electrician charges an initial fee of \$42.

Evaluate the statements

Let's check each statement:

1. "The electrician charges an initial fee of \$22." (False, the initial fee is \$42)
2. "The y-variable represents the number of hours." (False, \(y\) is the total charge)
3. "The electrician charges an initial fee of \$42." (True)
4. "The electrician charges \$22 for every hour worked." (True)
5. "The x-variable represents the electrician's charges in dollars." (False, \(x\) is hours)
6. "The electrician charges \$42 for every hour worked." (False, the hourly rate is \$22)

Answer:

• The electrician charges an initial fee of $22.
• The y-variable represents the number of hours.
• The electrician charges an initial fee of $42. (Correct answer)
• The electrician charges $22 for every hour worked. (Correct answer)
• The x-variable represents the electrician's charges in dollars.
• The electrician charges $42 for every hour worked.