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. $y

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, $y$, is directly related to the number of gallons that she put in the tank, $x$. The relationship between these two variables can be expressed using a linear equation.

The Equation of a Linear Relationship

A linear equation is a mathematical expression that describes a linear relationship between two variables. In this case, the linear equation will relate the total amount of gasoline in the tank, $y$, to the number of gallons that Jayne put in the tank, $x$. The general form of a linear equation is:

$$y = mx + b$$

where $m$ is the slope of the line and $b$ is the y-intercept.

Determining the Slope and Y-Intercept

To determine the slope and y-intercept of the linear equation, we need to consider the given information. Jayne already had 4 gallons of gas in her tank, and she put in an unknown number of gallons, $x$. The total amount of gasoline in the tank, $y$, is the sum of the initial amount of gas and the amount that Jayne put in the tank.

The slope of the line represents the rate of change of the total amount of gasoline in the tank with respect to the number of gallons that Jayne put in the tank. In this case, the slope is 1, since each additional gallon of gas that Jayne puts in the tank increases the total amount of gasoline in the tank by 1 gallon.

The y-intercept represents the initial amount of gas in the tank, which is 4 gallons.

The Linear Equation

Using the slope and y-intercept, we can write the linear equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that Jayne put in the tank, $x$:

$$y = x + 4$$

This equation states that the total amount of gasoline in the tank, $y$, is equal to the number of gallons that Jayne put in the tank, $x$, plus the initial amount of gas in the tank, which is 4 gallons.

Alternative Equation

Another way to write the linear equation is to use the equation:

$$y = 1x + 4$$

This equation is equivalent to the previous equation, but it uses a more formal notation to represent the slope and y-intercept.

Conclusion

In conclusion, the linear 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:

$$y = x + 4$$

This equation states that the total amount of gasoline in the tank, $y$, is equal to the number of gallons that Jayne put in the tank, $x$, plus the initial amount of gas in the tank, which is 4 gallons.

Final Answer

The final answer is:

y = x + 4$<br/> **Frequently Asked Questions (FAQs) About the Linear Equation** =========================================================== In the previous section, we discussed the linear equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that Jayne put in the tank, $x$. Here are some frequently asked questions (FAQs) about the linear equation: **Q: What is the slope of the linear equation?** -------------------------------------------- A: The slope of the linear equation is 1, which represents the rate of change of the total amount of gasoline in the tank with respect to the number of gallons that Jayne put in the tank. **Q: What is the y-intercept of the linear equation?** ----------------------------------------------- A: The y-intercept of the linear equation is 4, which represents the initial amount of gas in the tank. **Q: How do I use the linear equation to find the total amount of gasoline in the tank?** -------------------------------------------------------------------------------- A: To use the linear equation to find the total amount of gasoline in the tank, you need to know the number of gallons that Jayne put in the tank, $x$. Then, you can plug this value into the linear equation to find the total amount of gasoline in the tank, $y$. **Q: What if I don't know the number of gallons that Jayne put in the tank?** ------------------------------------------------------------------- A: If you don't know the number of gallons that Jayne put in the tank, you can't use the linear equation to find the total amount of gasoline in the tank. However, you can use the linear equation to find the number of gallons that Jayne put in the tank, $x$, if you know the total amount of gasoline in the tank, $y$. **Q: Can I use the linear equation to find the number of gallons that Jayne put in the tank if I know the total amount of gasoline in the tank?** --------------------------------------------------------- A: Yes, you can use the linear equation to find the number of gallons that Jayne put in the tank if you know the total amount of gasoline in the tank. To do this, you need to rearrange the linear equation to solve for $x$. **Q: How do I rearrange the linear equation to solve for $x$?** --------------------------------------------------------- A: To rearrange the linear equation to solve for $x$, you need to isolate $x$ on one side of the equation. You can do this by subtracting 4 from both sides of the equation and then dividing both sides of the equation by 1. **Q: What is the rearranged linear equation?** -------------------------------------------- A: The rearranged linear equation is: $x = y - 4

This equation states that the number of gallons that Jayne put in the tank, $x$, is equal to the total amount of gasoline in the tank, $y$, minus the initial amount of gas in the tank, which is 4 gallons.

Q: Can I use the linear equation to find the total amount of gasoline in the tank if I know the number of gallons that Jayne put in the tank?

A: Yes, you can use the linear equation to find the total amount of gasoline in the tank if you know the number of gallons that Jayne put in the tank. To do this, you need to plug the value of $x$ into the linear equation and solve for $y$.

Q: How do I plug the value of $x$ into the linear equation and solve for $y$?

A: To plug the value of $x$ into the linear equation and solve for $y$, you need to substitute the value of $x$ into the linear equation and then solve for $y$. You can do this by adding 4 to both sides of the equation.

Q: What is the final equation?

A: The final equation is:

$$y = x + 4$$

This equation states that the total amount of gasoline in the tank, $y$, is equal to the number of gallons that Jayne put in the tank, $x$, plus the initial amount of gas in the tank, which is 4 gallons.

Conclusion

In conclusion, the linear 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:

$$y = x + 4$$

This equation states that the total amount of gasoline in the tank, $y$, is equal to the number of gallons that Jayne put in the tank, $x$, plus the initial amount of gas in the tank, which is 4 gallons.

Final Answer

The final answer is:

$$y = x + 4$$