Final answer:
Ethan's service charge is captured by a linear equation y = 25 + 20x, where x is the independent variable representing hours worked, y is the dependent variable representing total earnings, the y-intercept is $25 (base fee), and the slope is $20 (hourly rate).
Step-by-step explanation:
The question pertains to the creation of a linear equation based on a scenario where an individual, Ethan, charges for services rendered with a base fee and an additional hourly rate. The linear equation that reflects Ethan's total earnings per visit is given by y = 25 + 20x. In this case, the independent variable is 'x', which represents the number of hours of work. The dependent variable is 'y', which denotes the total amount Ethan earns. The y-intercept of this equation is 25, which is the amount Ethan charges as a flat fee before any hourly charges apply. The slope is 20, indicating that for every hour of work, Ethan earns an additional $20 on top of the base fee. The interpretation of these values is critical for understanding the cost structure of Ethan's service.