A bike shop owner rents out bikes and scooters. The cost to rent a bike is $15 plus $8 per hour for each hour the bike is rented. The cost to rent a scooter is $35 plus $5 per hour for each hour the scooter is rented.

Which equation has a greater rate of change? The equation that represents the cost of renting a bike or the equation that represents the cost of renting a scooter.

A. The scooter rental has a rate of change of 35, which is greater than the rate of change of the bike rental.

B. The scooter rental has a rate of change of 40, which is greater than the rate of change of the bike rental.

C. The bike rental has a rate of change of 8, which is greater than the rate of change of the scooter rental.

D. The bike rental has a rate of change of 23, which is greater than the rate of change of the scooter rental.

Answer: C. The bike rental has a rate of change of 8, which is greater than the rate of change of the scooter rental.

Step-by-step explanation:

Let x represents the total number of hours and y represents the total cost of the vehicle after x hours.

According to the question,

The cost to rent a bike is $15 plus $8 per hour for each hour the bike is rented.

Thus, The total cost of renting bike after x hours,

y = 15 + 8 x

Similarly, The cost to rent a scooter is $35 plus $5 per hour for each hour the scooter is rented.

Thus, The total cost of renting scooter after x hours,

y = 35 + 5 x

Since, the slope-intercept of a line is, y = m x + c

Where m is the rate of change of the equation.

By the comparing the above equations with the slope-intercept of the line,

We get the rate of change of the equation, y = 15 + 8 x is 8

And, the rate of change of the equation, y = 35 + 5 x is 5.

Since, 8 > 5

Thus, The bike rental has a rate of change of 8, which is greater than the rate of change of the scooter rental.