Question

A travel agent studies examples of one-way airfares between cities across the United States. To predict any airfare, she proposes the formula A = 150 + 0.2x, in which A is the airfare in dollars and x is the distance of the flight in miles. Based on the formula, what is the difference in airfare between a flight of k miles and a flight of k + 1 miles?

1. thuhuong
The difference in airfare between a flight of k miles and a flight of k + 1 miles is 0.2.
We have the formula to predict the airfare between the cities as –
A = 150 + 0.2x
We have to determine the difference in airfare between a flight of k miles and a flight of k + 1 miles?

### What does the graph of the equation A = 150 + 0.2x represents ?

The equation given to us is –  A = 0.2(x) + 150 , which is similar to the equation – y = mx + c. Hence, the graph represents the straight line with slope m = 0.2.
We have the following equation –
A = 150 + 0.2x
The fare for the flight of K miles is –
A(K) = 150 + 0.2K                   (Eqn. 1)
and
for a flight of (K + 1) miles –
A(K + 1) = 150 + 0.2(K + 1) = 150 + 0.2K + 0.2 = (150 + 0.2K) + 0.2
From Eqn. 1 –  A(K) = 150 + 0.2K, Therefore –
A(K + 1) = A(K) + 0.2
A(K + 1) – A(K) = 0.2
Hence, the difference in airfare between a flight of k miles and a flight of k + 1 miles is 0.2.
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