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Answer :
To solve this problem, we need to interpret the function [tex]\( y = 22x + 42 \)[/tex], where [tex]\( y \)[/tex] represents the amount an electrician charges in dollars, and [tex]\( x \)[/tex] represents the number of hours worked. Let's break down each part of the function and analyze the statements:
1. Understanding the Function:
- The function is in the form of [tex]\( y = mx + b \)[/tex], which is a linear equation representing a straight line.
- Here, [tex]\( m = 22 \)[/tex] is the coefficient of [tex]\( x \)[/tex], representing the rate, which means the electrician charges [tex]$22 for each hour worked.
- The constant term \( b = 42 \) represents the initial amount charged before any work is done, often called the "initial fee".
2. Analyzing Each Statement:
- The electrician charges an initial fee of $[/tex]22.
- This is incorrect. The initial fee, found in the constant term of the function, is [tex]$42, not $[/tex]22.
- The electrician charges [tex]$22 for every hour worked.
- This is correct. The $[/tex]22 is the coefficient of [tex]\( x \)[/tex], indicating the charge per hour.
- The [tex]\( y \)[/tex]-variable represents the number of hours.
- This is incorrect. In the function [tex]\( y = 22x + 42 \)[/tex], [tex]\( y \)[/tex] represents the total charges in dollars, not the number of hours.
- The [tex]\( x \)[/tex]-variable represents the electrician's charges in dollars.
- This is incorrect. The [tex]\( x \)[/tex]-variable represents the number of hours worked, not the charge in dollars.
- The electrician charges an initial fee of [tex]$42.
- This is correct. As mentioned earlier, the constant term in the equation, $[/tex]42, represents the initial fee charged.
- The electrician charges [tex]$42 for every hour worked.
- This is incorrect. The charge per hour is $[/tex]22, not [tex]$42.
After analyzing all the statements, the correct statements are:
- The electrician charges $[/tex]22 for every hour worked.
- The electrician charges an initial fee of $42.
1. Understanding the Function:
- The function is in the form of [tex]\( y = mx + b \)[/tex], which is a linear equation representing a straight line.
- Here, [tex]\( m = 22 \)[/tex] is the coefficient of [tex]\( x \)[/tex], representing the rate, which means the electrician charges [tex]$22 for each hour worked.
- The constant term \( b = 42 \) represents the initial amount charged before any work is done, often called the "initial fee".
2. Analyzing Each Statement:
- The electrician charges an initial fee of $[/tex]22.
- This is incorrect. The initial fee, found in the constant term of the function, is [tex]$42, not $[/tex]22.
- The electrician charges [tex]$22 for every hour worked.
- This is correct. The $[/tex]22 is the coefficient of [tex]\( x \)[/tex], indicating the charge per hour.
- The [tex]\( y \)[/tex]-variable represents the number of hours.
- This is incorrect. In the function [tex]\( y = 22x + 42 \)[/tex], [tex]\( y \)[/tex] represents the total charges in dollars, not the number of hours.
- The [tex]\( x \)[/tex]-variable represents the electrician's charges in dollars.
- This is incorrect. The [tex]\( x \)[/tex]-variable represents the number of hours worked, not the charge in dollars.
- The electrician charges an initial fee of [tex]$42.
- This is correct. As mentioned earlier, the constant term in the equation, $[/tex]42, represents the initial fee charged.
- The electrician charges [tex]$42 for every hour worked.
- This is incorrect. The charge per hour is $[/tex]22, not [tex]$42.
After analyzing all the statements, the correct statements are:
- The electrician charges $[/tex]22 for every hour worked.
- The electrician charges an initial fee of $42.
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