Answer :
To solve the problem and determine the correct equation of a line that models the amount of money Niall will have after paying back his cousin, we need to consider a few key points:
1. Initial Debt: Niall owes his cousin [tex]$187. This means any money he earns first goes to paying back this debt.
2. Earnings from Painting: Niall earns $[/tex]34 for every 2 hours he spends painting. To find how much he earns per hour, we divide [tex]$34 by 2, which gives us $[/tex]17 per hour.
3. Equation of the Line:
- We want to express the total amount of money Niall will have, [tex]\( y \)[/tex], in terms of the number of hours, [tex]\( x \)[/tex], he works.
- Since he earns [tex]$17 per hour, the part of the equation representing his earnings is \( 17x \).
- Initially, he is in debt by $[/tex]187. So, before he can have any positive money, he must pay this debt. This starts him off with [tex]\( -187 \)[/tex].
Putting it all together, the equation that models this situation is:
[tex]\[ y = 17x - 187 \][/tex]
Therefore, the correct answer is:
D. [tex]\( y = 17x - 187 \)[/tex]
1. Initial Debt: Niall owes his cousin [tex]$187. This means any money he earns first goes to paying back this debt.
2. Earnings from Painting: Niall earns $[/tex]34 for every 2 hours he spends painting. To find how much he earns per hour, we divide [tex]$34 by 2, which gives us $[/tex]17 per hour.
3. Equation of the Line:
- We want to express the total amount of money Niall will have, [tex]\( y \)[/tex], in terms of the number of hours, [tex]\( x \)[/tex], he works.
- Since he earns [tex]$17 per hour, the part of the equation representing his earnings is \( 17x \).
- Initially, he is in debt by $[/tex]187. So, before he can have any positive money, he must pay this debt. This starts him off with [tex]\( -187 \)[/tex].
Putting it all together, the equation that models this situation is:
[tex]\[ y = 17x - 187 \][/tex]
Therefore, the correct answer is:
D. [tex]\( y = 17x - 187 \)[/tex]
