Let's define the variables first:

• Let $y$ represent the amount of gas left in the car after $x$ hours.
• Let $x$ represent the number of hours into the trip.

Equation:

At the beginning of the trip, there are 18 gallons of gas, and for every hour that passes, 2.5 gallons are used. The amount of gas left decreases by 2.5 gallons each hour. Therefore, the equation is:

$y = 18 - 2.5x$

Where:

• $y$ is the amount of gas left in the car after $x$ hours.
• $x$ is the number of hours into the trip.

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a) What is the rate of change?

The rate of change is the amount of gas used per hour, which is $-2.5$ gallons per hour.

$\text{Rate of change} = -2.5 \, \text{gal/hour}$

b) What is the initial value?

The initial value is the amount of gas in the car at the beginning of the trip, which is 18 gallons.

$\text{Initial value} = 18 \, \text{gallons}$

Would you like more details or have any questions?

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Here are five related questions:

1. After 4 hours, how much gas is left in the car?
2. How many hours can the car run before all the gas is used up?
3. What does the slope of the equation represent in this context?
4. If the car starts with 25 gallons instead of 18, how would the equation change?
5. How much gas is left after 6 hours?

Tip: In linear equations, the initial value is always the $y$-intercept, while the rate of change is the slope of the line.