Writing Equations of lines- Word problem.

Question

In 1998, an airline offered a special airfare of $201 to fly from Cincinnati to Washington D.C., a distance of 386 miles. Special airfares offered for longer flights increased by about $.138 per mile. Write a linear model for the special airfares ("a") based on the total number of miles ("t") of the flight. Estimate the airfare offered for a flight from Boston to Sacramento, a distance of 2629 miles.

Answer 1

So you need to draw a linear graph with a slope representing the number of dollars per mile. The “t”-axis will represent the distance in miles, and the “a”-axis will represent the airfare in dollars.

The point you are given is (386, 201)

The point you need to figure out is (2629, ?)

The slope (m) of the line is 0.138 (cost increase in dollars per mile).

Then you will need to modify the line equation (y=mx+b). Since you are asked to write a linear model for the special airfares ("a") based on the total number of miles ("t") of the flight, you'll want to substitute "a" for "y" and "t" for "x"

So, the equation of the line is a = 0.138t + b. We need to figure out what "b" is.

Putting in the point given gives  201 = 386 (0.138) + b, so b = 147.73. The equation for this particular line is:

a = 0.138t + 147.73.

Putting in the value  t = 2629 (the distance from Boston to Sacramento) gives  a = 0.138 (2629) + 147.73, or  a = 510.53.

The fare from Boston to Sacramento is therefore $510.53