Select the correct answer.

Niall owes [tex]\$187[/tex] to his cousin. However, he doesn't have any money right now. He hopes to earn some money by painting a house. He gets paid [tex]\$34[/tex] for every 2 hours he paints. Which equation of a line models [tex]y[/tex], the amount of money he will have after paying back his cousin, in terms of [tex]x[/tex], the number of hours he spends painting?

A. [tex]y = 34x - 187[/tex]

B. [tex]y = 17x + 187[/tex]

C. [tex]y = 34x + 187[/tex]

D. [tex]y = 17x - 187[/tex]

Niall earns \[tex]$34 for every 2 hours of work. First, we determine his hourly earnings. This is calculated by dividing \$[/tex]34 by 2 hours:

[tex]$$
\text{Hourly rate} = \frac{34}{2} = 17 \text{ dollars per hour}.
$$[/tex]

Since Niall owes \[tex]$187, he effectively starts with $-187$ dollars. Every hour he paints, he earns an additional \$[/tex]17. Therefore, if he paints for [tex]$x$[/tex] hours, his total money after paying back his cousin is given by:

[tex]$$
y = 17x - 187.
$$[/tex]

Thus, the equation that models the situation is:

[tex]$$
\boxed{y = 17x - 187}.
$$[/tex]

This corresponds to option D.