Answer :
To solve this problem, we need to understand how much money Niall makes per hour and how this affects the amount of money he will have after repaying his [tex]$187 debt to his cousin.
1. Determine the payment per hour:
- Niall is paid $[/tex]34 for every 2 hours of painting.
- To find his hourly rate, divide [tex]$34 by 2.
- Calculation: $[/tex]34 ÷ 2 = [tex]$17 per hour.
2. Formulate the equation:
- We need an equation that represents the total amount of money Niall has after paying back his cousin. The general form of a linear equation is \( y = mx + b \), where:
- \( y \) is the total amount of money after repaying the debt.
- \( m \) is the amount earned per one hour, which we found to be $[/tex]17.
- [tex]\( x \)[/tex] is the number of hours he paints.
- [tex]\( b \)[/tex] is the initial amount of money, considering the debt here as a negative value since it's money owed. So, it's [tex]\(-187\)[/tex].
3. Write the equation:
- Considering the hourly rate and the debt, the equation becomes:
- [tex]\( y = 17x - 187 \)[/tex]
So, the correct equation of the line that models the amount of money Niall will have after paying back his cousin, in terms of the number of hours he spends painting, is:
y = 17x - 187
Hence, the correct answer is option D: [tex]\( y = 17x - 187 \)[/tex].
1. Determine the payment per hour:
- Niall is paid $[/tex]34 for every 2 hours of painting.
- To find his hourly rate, divide [tex]$34 by 2.
- Calculation: $[/tex]34 ÷ 2 = [tex]$17 per hour.
2. Formulate the equation:
- We need an equation that represents the total amount of money Niall has after paying back his cousin. The general form of a linear equation is \( y = mx + b \), where:
- \( y \) is the total amount of money after repaying the debt.
- \( m \) is the amount earned per one hour, which we found to be $[/tex]17.
- [tex]\( x \)[/tex] is the number of hours he paints.
- [tex]\( b \)[/tex] is the initial amount of money, considering the debt here as a negative value since it's money owed. So, it's [tex]\(-187\)[/tex].
3. Write the equation:
- Considering the hourly rate and the debt, the equation becomes:
- [tex]\( y = 17x - 187 \)[/tex]
So, the correct equation of the line that models the amount of money Niall will have after paying back his cousin, in terms of the number of hours he spends painting, is:
y = 17x - 187
Hence, the correct answer is option D: [tex]\( y = 17x - 187 \)[/tex].
