To solve this problem, we need to express Esther's monthly pay rate using a linear equation. We are given two key pieces of information:
1. Esther earns [tex]$12 per hour.
2. Esther receives an additional $[/tex]50 travel allowance every month.
We need to formulate a linear equation in the form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( y \)[/tex] is the total monthly pay.
- [tex]\( x \)[/tex] is the number of hours Esther works in a month.
- [tex]\( m \)[/tex] is the hourly pay rate.
- [tex]\( b \)[/tex] is the fixed monthly travel allowance.
Let’s break it down step by step:
1. Hourly Pay Calculation:
Esther earns [tex]$12 for each hour she works. So, if she works \( x \) hours in a month, her earnings from hours worked can be represented as \( 12x \).
2. Fixed Monthly Allowance:
Regardless of how many hours Esther works, she always receives an additional $[/tex]50 each month as a travel allowance. This is a constant amount, represented by [tex]\( b \)[/tex] in the equation, where [tex]\( b = 50 \)[/tex].
Combining these two components (hourly earnings and the fixed allowance) into the linear equation form, we get:
[tex]\[ y = 12x + 50 \][/tex]
Now, let’s compare this to the options provided:
A. [tex]\( y = 50x + 12 \)[/tex]
B. [tex]\( y = 12x + 50 \)[/tex]
C. [tex]\( y = 12x \)[/tex]
D. [tex]\( y = 50x \)[/tex]
The correct equation that matches our derived equation ([tex]\( y = 12x + 50 \)[/tex]) is option:
B. [tex]\( y = 12x + 50 \)[/tex]
Thus, the correct answer is [tex]\( \boxed{2} \)[/tex].
