Question

Sophia is starting a tutoring service to make some extra money. She plans to charge $8.50 per hour plus a base fee of $12. Write a function that could be used to represent her total charge for tutoring, y, as a function of the number of hours she tutors, x.

a) y = 8.50x
b) y = 12 + 8.50x
c) y = 12x + 8.50
d) y = 12x - 8.50

Answer 1

Sophia's total charge for tutoring as a function of hours tutored is represented by the equation y = 12 + 8.50x, where 12 is the base fee and 8.50 is the charge per hour.

Step-by-step explanation:

To represent Sophia's total charge for tutoring y as a function of the number of hours she tutors x, we need to account for both her hourly rate and her base fee. Sophia's hourly rate is $8.50 per hour, and she has a base fee of $12. For every hour she tutors, she earns an additional $8.50, and this is regardless of how many hours she tutors. Therefore, the equation to represent her total charge is:

y = 12 + 8.50x

This equation means that Sophia charges a one-time fee of $12 at the start of the tutoring session (when x = 0), which is the y-intercept. The slope is $8.50, indicating she charges $8.50 for each hour of tutoring. The correct function from the choices is therefore b) y = 12 + 8.50x.