Question

A jetliner uses 3,600 gallons of fuel per hour while it is cruising, and there are 15,000 gallons of fuel in the jetliner's fuel tank when it begins to cruise. If y represents the amount of fuel, in thousands of gallons, remaining in the fuel tank after the jetliner cruises for x hours, determine the graph of the solution set for this situation and the equation modeled by the graph.

Answer 1

Top LEFT graph

y = 15 - 3.6x

Explanation:

slope = m = -3.6 thousand gallons/hr

y-intercept = b = 15

equation in y = mx + b form:

y = 15 - 3.6x

The only graph that represents this equation is the one on the top left

Answer 2

top left graph

y = 15 - 3.6x

Explanation:

let time (in hours) = x

let y = number of thousands gallons left in tank after x hours of travel

y = mx + b

initial amount of fuel = 15

y = mx + 15

fuel consumption is 3.6 thousands of gal/hour, so m = -3.6

y = -3.6x + 15

The tank starts at x = 0 full with 15,000 gallons, so at x = 0, y = 15.

The y-intercept of the graph must be 15.

That eliminates the two bottom graphs.

The number of hours that 15,000 gallons last is:

15000/3600 = 4.1666...,

or approximately 4.2 hours.

At 4.2 hours, the amount of fuel is 0, so we have the point (4.2, 0).

Answer: top left graph