To determine the graph of the solution set for this situation and the equation modeled by the graph, follow these steps:
1. Identify the initial amount of fuel:
The jetliner starts with 15,000 gallons of fuel in its tank.
2. Determine the fuel usage rate:
The jetliner uses 3,600 gallons of fuel per hour.
3. Define the variables:
Let [tex]\( x \)[/tex] represent the number of hours the jetliner has been cruising.
Let [tex]\( y \)[/tex] represent the amount of fuel remaining in the tank in thousands of gallons.
4. Write the equation for the remaining fuel in gallons:
The remaining fuel after [tex]\( x \)[/tex] hours can be calculated by subtracting the total fuel used from the initial amount:
[tex]\[
\text{Remaining fuel in gallons} = 15000 - 3600x
\][/tex]
5. Convert the remaining fuel to thousands of gallons:
Since [tex]\( y \)[/tex] represents the remaining fuel in thousands of gallons, divide the remaining fuel by 1,000:
[tex]\[
y = \frac{15000 - 3600x}{1000}
\][/tex]
6. Simplify the equation:
Divide the numerator by 1,000:
[tex]\[
y = 15 - 3.6x
\][/tex]
Therefore, the equation that models the graph for the remaining fuel in the jetliner's tank in thousands of gallons after [tex]\( x \)[/tex] hours of cruising is:
[tex]\[
y = 15 - 3.6x
\][/tex]
Among the given options, the correct equation is:
[tex]\[
y = 15 - 3.6x
\][/tex]
