Question

A taxi's fare can be modeled by a linear function based on an initial charge for each ride plus a rate for each mile of the ride. The charge for a 2-mile ride is $10. The charge for a 5-mile ride is $19. What is the rate for each mile of the ride?

a. $4
b. $3
c. $2.50
d. $5

Answer 1

To determine the taxi's rate per mile, two rides were analyzed: a 2-mile ride costing $10 and a 5-mile ride costing $19. By setting up a linear equation and solving for the slope (rate per mile), it was found that the rate is $3 per mile.

Step-by-step explanation:

To find the rate per mile for the taxi's ride, we can set up and solve a linear equation. We have two points that represent the cost for a given number of miles: (2, $10) and (5, $19). The general form of the equation for this linear function is y = mx + b, where y is the total charge, m is the rate per mile, x is the number of miles, and b is the initial charge. By plugging in the coordinates of our two points, we can create a system of equations to solve for m and b.

Using the first point (2, $10):
10 = 2m + b (1)
Using the second point (5, $19):
19 = 5m + b (2)
Now, by subtracting equation (1) from equation (2), we can eliminate b and solve for m.

19 - 10 = 5m - 2m
9 = 3m
m = 3

Therefore, the rate per mile for the ride is $3, which corresponds to option b.