Jayne Stopped To Get Gas Before Going On A Road Trip. The Tank Already Had 4 Gallons Of Gas In It. Which Equation Relates The Total Amount Of Gasoline In The Tank, $y$, To The Number Of Gallons That She Put In The Tank, $x$?A.

Mar 9, 2025 by ADMIN 231 views

**Understanding the Relationship Between Gasoline and the Number of Gallons**

When Jayne stopped to get gas before going on a road trip, she already had 4 gallons of gas in her tank. To determine the total amount of gasoline in the tank, we need to consider the number of gallons that she put in the tank. In this scenario, the total amount of gasoline in the tank, denoted as $y$, is directly related to the number of gallons that she put in the tank, denoted as $x$. The relationship between these two variables can be expressed using a mathematical equation.

The Equation of Total Gasoline in the Tank

The equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that she put in the tank, $x$, is given by:

y = x + 4

Explanation of the Equation

In this equation, $y$ represents the total amount of gasoline in the tank, and $x$ represents the number of gallons that Jayne put in the tank. The constant term, 4, represents the initial amount of gasoline in the tank. When Jayne puts $x$ gallons of gas in the tank, the total amount of gasoline in the tank becomes $x + 4$ gallons.

Interpretation of the Equation

The equation $y = x + 4$ can be interpreted as follows:

If Jayne puts 0 gallons of gas in the tank, the total amount of gasoline in the tank will be 4 gallons.
If Jayne puts 1 gallon of gas in the tank, the total amount of gasoline in the tank will be 5 gallons.
If Jayne puts 2 gallons of gas in the tank, the total amount of gasoline in the tank will be 6 gallons.
And so on.

Graphical Representation of the Equation

The equation $y = x + 4$ can be represented graphically as a straight line with a slope of 1 and a y-intercept of 4. The graph will have a constant rate of change, indicating that for every additional gallon of gas that Jayne puts in the tank, the total amount of gasoline in the tank will increase by 1 gallon.

Conclusion

In conclusion, the equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that Jayne put in the tank, $x$, is given by $y = x + 4$. This equation can be interpreted as a linear relationship between the total amount of gasoline in the tank and the number of gallons that Jayne puts in the tank. The equation can also be represented graphically as a straight line with a slope of 1 and a y-intercept of 4.

Real-World Applications

The equation $y = x + 4$ has several real-world applications, including:

Calculating the total amount of gasoline in a tank based on the number of gallons that have been added.
Determining the amount of gasoline that needs to be added to a tank to reach a certain level.
Calculating the cost of gasoline based on the number of gallons that have been added.

Example Problems

Here are some example problems that illustrate the use of the equation $y = x + 4$:

If Jayne puts 2 gallons of gas in the tank, what is the total amount of gasoline in the tank?
If Jayne wants to add 5 gallons of gas to the tank, how much gasoline will be in the tank?
If Jayne puts 1 gallon of gas in the tank, what is the total amount of gasoline in the tank?

Solutions to Example Problems

Here are the solutions to the example problems:

If Jayne puts 2 gallons of gas in the tank, the total amount of gasoline in the tank will be $2 + 4 = 6$ gallons.
If Jayne wants to add 5 gallons of gas to the tank, the total amount of gasoline in the tank will be $5 + 4 = 9$ gallons.
If Jayne puts 1 gallon of gas in the tank, the total amount of gasoline in the tank will be $1 + 4 = 5$ gallons.

Conclusion

In our previous article, we explored the equation $y = x + 4$, which relates the total amount of gasoline in the tank, $y$, to the number of gallons that Jayne put in the tank, $x$. In this article, we will answer some frequently asked questions about the equation and its applications.

Q: What is the initial amount of gasoline in the tank?

A: The initial amount of gasoline in the tank is 4 gallons. This is represented by the constant term, 4, in the equation $y = x + 4$.

Q: How does the equation change if the initial amount of gasoline in the tank is different?

A: If the initial amount of gasoline in the tank is different, the equation will change accordingly. For example, if the initial amount of gasoline in the tank is 6 gallons, the equation would be $y = x + 6$.

Q: What happens if Jayne puts a negative number of gallons in the tank?

A: If Jayne puts a negative number of gallons in the tank, the equation will still work, but the result will be a negative number. For example, if Jayne puts -2 gallons in the tank, the total amount of gasoline in the tank will be $-2 + 4 = 2$ gallons.

Q: Can the equation be used to calculate the number of gallons that need to be added to the tank to reach a certain level?

A: Yes, the equation can be used to calculate the number of gallons that need to be added to the tank to reach a certain level. For example, if Jayne wants to add enough gasoline to the tank to reach a total of 10 gallons, she would need to add $10 - 4 = 6$ gallons to the tank.

Q: How does the equation relate to the cost of gasoline?

A: The equation $y = x + 4$ can be used to calculate the cost of gasoline based on the number of gallons that have been added. For example, if the cost of gasoline is $2 per gallon, the total cost of gasoline in the tank would be $2x + 8$ dollars.

Q: Can the equation be used to calculate the amount of gasoline that has been used?

A: Yes, the equation can be used to calculate the amount of gasoline that has been used. For example, if Jayne starts with 4 gallons of gasoline in the tank and ends up with 2 gallons of gasoline in the tank, she has used $4 - 2 = 2$ gallons of gasoline.

Q: What are some real-world applications of the equation?

A: Some real-world applications of the equation $y = x + 4$ include:

Calculating the total amount of gasoline in a tank based on the number of gallons that have been added.
Determining the amount of gasoline that needs to be added to a tank to reach a certain level.
Calculating the cost of gasoline based on the number of gallons that have been added.
Calculating the amount of gasoline that has been used.

Q: Can the equation be used to solve problems involving multiple tanks?

A: Yes, the equation can be used to solve problems involving multiple tanks. For example, if Jayne has two tanks, one with 4 gallons of gasoline and one with 6 gallons of gasoline, and she wants to add 2 gallons of gasoline to the first tank, the total amount of gasoline in the first tank will be $2 + 4 = 6$ gallons, and the total amount of gasoline in the second tank will be $6 + 2 = 8$ gallons.

Conclusion

In conclusion, the equation $y = x + 4$ is a powerful tool for calculating the total amount of gasoline in a tank based on the number of gallons that have been added. The equation can be used to solve a variety of problems, including calculating the cost of gasoline, determining the amount of gasoline that needs to be added to a tank to reach a certain level, and calculating the amount of gasoline that has been used.