Select the correct answer.

Niall owes [tex]\$187[/tex] to his cousin. 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]

We begin by finding Niall's hourly wage. He earns \[tex]$34 for every 2 hours of work, so his hourly rate is

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

If we let $[/tex]x[tex]$ represent the number of hours he paints, then the total amount he earns from painting is

$[/tex][tex]$17x.$[/tex][tex]$

Since he owes \$[/tex]187 to his cousin, after paying off his debt, the amount of money he will have is given by

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

Thus, the correct equation is option D:

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