Final answer:
The relationship between hours worked and income for Gilbert, who earns $7.50 per hour, and Ethan, who charges $25 plus $20 per hour, can be depicted with linear equations. For Ethan's case, the independent variable is hours worked, the dependent variable is total earnings, the y-intercept is the flat fee for each visit, and the slope is his hourly rate.
Step-by-step explanation:
The question involves graphing the relationship between hours worked and total income earned, which is a topic in algebra, specifically dealing with linear functions and graphing. If Gilbert earns $7.50 per hour washing cars, we have a simple linear equation that describes his earnings: y = 7.5x, where y represents the total amount of money earned and x represents the number of hours worked.
For the scenario given in the Try It Σ example, concerning Ethan, his income per repair visit can be represented by the linear equation y = 25 + 20x. The independent variable is x (the number of hours he works), and the dependent variable is y (the total amount he earns). The y-intercept is $25 (the flat fee for each visit), and the slope is $20 (the amount Ethan earns per hour of work). The y-intercept represents the minimum charge for a visit, and the slope represents the hourly rate.