Answer :
We are given that Niall owes \[tex]$187 to his cousin, so his starting balance is:
$[/tex][tex]$-187.$[/tex][tex]$
He earns \$[/tex]34 for every 2 hours of painting. Thus, his hourly rate is:
[tex]$$\frac{34}{2} = 17 \text{ dollars per hour}.$$[/tex]
Since he earns money at a constant rate (a linear relationship), we can model the total amount of money he has (after paying back his cousin) with the linear equation in slope-intercept form:
[tex]$$y = mx + b,$$[/tex]
where
- [tex]$m$[/tex] is the hourly rate (slope), and
- [tex]$b$[/tex] is the starting balance (y-intercept).
Substituting the values we have:
[tex]$$y = 17x - 187.$$[/tex]
Thus, the equation that models his total amount of money after painting for [tex]$x$[/tex] hours is:
[tex]$$\boxed{y = 17x - 187}.$$[/tex]
This corresponds to option D.
$[/tex][tex]$-187.$[/tex][tex]$
He earns \$[/tex]34 for every 2 hours of painting. Thus, his hourly rate is:
[tex]$$\frac{34}{2} = 17 \text{ dollars per hour}.$$[/tex]
Since he earns money at a constant rate (a linear relationship), we can model the total amount of money he has (after paying back his cousin) with the linear equation in slope-intercept form:
[tex]$$y = mx + b,$$[/tex]
where
- [tex]$m$[/tex] is the hourly rate (slope), and
- [tex]$b$[/tex] is the starting balance (y-intercept).
Substituting the values we have:
[tex]$$y = 17x - 187.$$[/tex]
Thus, the equation that models his total amount of money after painting for [tex]$x$[/tex] hours is:
[tex]$$\boxed{y = 17x - 187}.$$[/tex]
This corresponds to option D.
