Final answer:
The correct equation representing the plumber's total fee is c = 65 + 20h, which includes a flat rate of $65 plus $20 for each hour of labor.
Step-by-step explanation:
The correct equation to determine the total fee charged by the plumber, where h represents the number of hours the plumber spent fixing the problem and c represents the total charge, is c = 65 + 20h. This is because the plumber charges a flat rate of $65 for coming to the house, represented by the constant term, and an hourly rate of $20, represented by the variable term multiplied by h. The flat rate is the initial cost regardless of the time spent, while the hourly rate gets multiplied by the number of hours worked, which may vary. Since this structure is consistent with the way other service-based charges are represented in linear equations, such as repair fees or tutoring sessions, the equation c = 65 + 20h reflects the fixed cost plus the variable hourly cost.