The linear function representing Jack's pay is f(x) = 10x + 8. It accurately models his earnings for each hour worked, as evidenced by satisfying the given data points (1, 18) and (2, 28). Option D is the correct answer.
To find the linear function representing Jack's pay, we can use the given data points (hours, pay). Let's substitute two points into each option and see which one satisfies both:
Given points: (1, 18) and (2, 28)
A. f(x) = 10x + 8: f(1) = 10(1) + 8 = 18, f(2) = 10(2) + 8 = 28 (Satisfied)
B. f(x) = 15x + 3: f(1) = 15(1) + 3 = 18, f(2) = 15(2) + 3 = 33 (Not satisfied)
C. f(x) = 0.5x + 1: f(1) = 0.5(1) + 1 = 1.5, f(2) = 0.5(2) + 1 = 2 (Not satisfied)
D. f(x) = x + 18: f(1) = 1 + 18 = 19, f(2) = 2 + 18 = 20 (Not satisfied)
The correct linear function is A. f(x) = 10x + 8.
The complete question is:
Jack works after school. each day he earns a set amount, plus an hourly wage.
hours- 1 1.5 2 2.5 3
pay- 18 23 28 33 38
Choose the linear function f Jack can use to find his pay.
A. f(x) = 10x + 8
B. f(x) = 15x + 3
C. f(x) = 0.5x + 1
D. f(x) = x + 18