Final answer:
The equation that represents the amount the rental car company will charge for any number of days is y = 20x + 15, where y is the total charge and x is the number of days rented. The slope of 20 indicates the daily rate, and the y-intercept of 15 represents an initial charge.
Step-by-step explanation:
To find the equation that represents the amount the rental car company will charge for any number of days, we need to determine the daily rate and the initial charge, if any. To do this, we can use the two given rental scenarios: $75 for a 3-day rental and $155 for a 7-day rental.
Let's denote y as the total charge and x as the number of days rented. We have two points based on the information given: (3, 75) and (7, 155). Using these points, we calculate the slope (daily rate) by dividing the difference in total charges by the difference in days:
Slope = (155 - 75) / (7 - 3) = 80 / 4 = 20
This means the company charges $20 per day. Next, we need to find the y-intercept, which represents the initial charge when x is 0. To do this, we can use one of the points and the slope:
75 = 20(3) + b
75 = 60 + b
b = 15
Therefore, the y-intercept is $15. The final equation is y = 20x + 15. This equation means the rental car company will charge $20 per day plus an initial fee of $15.