Final answer:
Ethan's salary can be represented by a piecewise linear graph with a slope of $16 per hour for up to 40 hours and a slope of $24 per hour for 40 to 60 hours, with a change in slope at 40 hours.
Step-by-step explanation:
The question you've asked pertains to how to represent Ethan's weekly salary based on the number of hours he works at his summer job, using a graph. Since the pay rate changes after 40 hours, the function representing his salary will have two segments. For the first 40 hours, Ethan earns $16 per hour. After 40 hours, up to a maximum of 60 hours, Ethan earns $24 per hour. The graph would therefore be a piecewise linear function with a slope of $16 per hour up to 40 hours and a steeper slope of $24 per hour from 40 to 60 hours. At 40 hours, there would be a change in the slope of the line, indicating the shift in pay rate.
The graph should start at $0 income when he works 0 hours and increase linearly until 40 hours. Beyond 40 hours, the graph should show a change in slope, reflecting the increase in his hourly rate to $24 per hour, until it caps at 60 hours, after which the function should remain constant, assuming he cannot work more than 60 hours.