Question

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.

Answer 1

Only two are correct;

a) The electrician charges an initial fee of $42

b) The electrician charges $22 for every hour worked

Explanation:

Here, we want to select all possible correct options;

Kindly understand that the equation of a straight line can be represented in the form;

y = mx + c

where m is the slope and c is the y-intercept (where x = 0)

1. The electrician charges an initial fee of $22

This is wrong. $22 represents the slope and it indicates a rate of change and not an initial fee

2. The y-variable represents the number of hours

This is wrong. What the y-variable represents is the amount charged in US dollars

3. The electrician charges an initial fee of $42

This is correct. The y-intercept value is the value when x is zero

4. The electrician charges $22 for every hour worked

This is correct. From the equation, 22 represents the change which is the slope

It is the amount charged per hour

5. The x-variable represents the electrician’s charges in dollars

This is wrong. As we can see from the question, the x-variable represents the number of hours

6. The electrician charges $42 for every hour worked

This is wrong. What $42 represents is the charge at 0 hour which means the charge at x = 0