y = 19.99 + 1.50x
The equation above models the total cost y, in dollars, that a company charges a customer to rent a truck for one day and drive the truck x miles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the xy-plane, what does the y-intercept of the graph represent in terms of the model?

Options

A. A flat fee of $19.99
B. A charge per mile of $1.50
C. A charge per mile of $19.99
D. Total daily charges of $21.49

Answer

A

Explanation

The y-intercept of the graph of y = 19.99 + 1.50x in the xy-plane is the point on the graph with an x-coordinate equal to 0. In the model represented by the equation, the x-coordinate represents the number of miles a rental truck is driven during a one-day rental, and so the y-intercept represents the charge, in dollars, for the rental when the truck is driven 0 miles, that is, the y-intercept represents the cost, in dollars, of the flat fee. Since the y-intercept of the graph of y = 19.99 + 1.50x is (0, 19.99), the y-intercept represents a flat fee of $19.99 in terms of the model.
Choice B is incorrect. The slope of the graph of y = 19.99 + 1.50x in the xy-plane, not the y-intercept, represents a driving charge per mile of $1.50 in terms of the model. Choice C is incorrect. Since the coefficient of x in the equation is 1.50, the charge per mile for driving the rental truck is $1.50, not $19.99. Choice D is incorrect. The sum of 19.99 and 1.50, which is 21.49, represents the cost, in dollars, for renting the truck for one day and driving the truck 1 mile, however, the total daily charges for renting the truck does not need to be $21.49.