Question

Juan earns $7 per hour plus $20 per week making picture frames.

a. Write a function g(x) for Juan's total earnings if he works x hours in one week.

b. Without graphing the function, determine the slope.

c. Describe the meaning of the slope within the context of Juan's job.

Options:
Option 1: The function g(x) is g(x) = 7x + 20.
Option 2: The function g(x) is g(x) = 20x + 7.
Option 3: The function g(x) is g(x) = 7x - 20.
Option 4: The function g(x) is g(x) = 20 - 7x.

Answer 1

The function for Juan's total earnings when working x hours in one week is g(x) = 7x + 20 (Option 1), with a slope of 7. The slope indicates that Juan earns an additional $7 for every additional hour worked.

Step-by-step explanation:

To answer the student's question, let's start with part a:

The function g(x) for Juan's total earnings if he works x hours in one week can be determined by considering the fixed amount he earns per week ($20) plus the amount he earns per hour worked ($7 per hour).

Thus, the correct equation would be g(x) = 7x + 20, which corresponds to Option 1.

For part b, the slope of the function g(x) = 7x + 20 is the coefficient of x, which in this case is 7.

Finally, in part c, within the context of Juan's job, the slope represents the rate at which Juan's earnings increase for each additional hour worked. Therefore, for every extra hour that Juan works, he earns an additional $7.