Questions: The cost, c(x), for parking in a hospital lot is given by c(x)=5x+3.00, where x is the number of hours. What does the slope mean in this situation? A. The rate of change of the cost of parking in the lot is 5.00 per hour. B. It costs a total of 5.00 to park in the lot. C. Parking in the lot costs 3.00 per car. D. The rate of change of the cost of parking in the lot is 3.00 per hour.

Solution Steps

The given equation for the cost of parking is \( c(x) = 5x + 3.00 \). This is a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

In the equation \( c(x) = 5x + 3.00 \), the slope \( m \) is 5. The slope represents the rate of change of the cost with respect to the number of hours parked. Therefore, the slope of 5 means that the cost increases by \$5.00 for each additional hour of parking.

Now, we need to match our interpretation of the slope with the given multiple-choice options:

• A. The rate of change of the cost of parking in the lot is \$5.00 per hour.
• B. It costs a total of \$5.00 to park in the lot.
• C. Parking in the lot costs \$3.00 per car.
• D. The rate of change of the cost of parking in the lot is \$3.00 per hour.

Option A correctly describes the meaning of the slope as the rate of change of the cost of parking, which is \$5.00 per hour.

Final Answer