Question

Benji noticed that when he took a taxicab ride for 4 miles he paid $13.40 and when he rode for 7 miles he paid $21.50. This data can be represented by two points where a is the number of miles ridden and y is the cost in dollars. a. What does the slope of the line connecting these two points represent in the context of this problem? b. Find the slope of the line.

Answer 1

The slope represents the additional cost per mile, which is $2.70 for every mile traveled. It is found using the slope formula based on two points representing miles and cost for Benji's taxi rides.

Step-by-step explanation:

Benji's taxi fare problem can be analyzed by first establishing the two points representing his taxi rides. The first point is (4, 13.40) and the second is (7, 21.50), where the first value in each pair represents miles (independent variable 'a') and the second value represents cost (dependent variable 'y').

a. Slope Interpretation

The slope of a line in this context represents the rate of change in the taxi fare with respect to the distance traveled. In simpler terms, it is the additional cost per mile, which is consistent over the distance of the ride.

b. Calculating the Slope

The slope (m) can be calculated using the formula m = (y2 - y1) / (a2 - a1), where (a1, y1) and (a2, y2) are the two points. Plugging in our values, we get:

m = (21.50 - 13.40) / (7 - 4)

m = 8.10 / 3

m = 2.70

Therefore, the slope of the line is 2.70, which means Benji pays an additional $2.70 for every mile he travels in the taxi.