Complete The Coordinate Table For The Given Equation $xy = -4$.| X | Y ||----|----|| 1 | || 2 | || -1 | || -2 | |

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Introduction

In mathematics, coordinate tables are used to represent the relationship between two variables. Given an equation, we can use a coordinate table to find the corresponding values of the variables. In this article, we will focus on completing the coordinate table for the given equation $xy = -4$. This equation represents a hyperbola, and we will use the table to find the values of $x$ and $y$ that satisfy the equation.

Understanding the Equation

The given equation is $xy = -4$. This equation represents a hyperbola, which is a type of curve that has two branches. The equation can be rewritten as $y = -\frac{4}{x}$, which represents a hyperbola with a horizontal asymptote at $y = 0$. The equation has two solutions, $x = 2$ and $x = -2$, which correspond to the points $(2, -2)$ and $(-2, 2)$.

Completing the Coordinate Table

To complete the coordinate table, we need to find the values of $x$ and $y$ that satisfy the equation $xy = -4$. We can start by plugging in the values of $x$ and $y$ into the equation and solving for the other variable.

x = 1

If $x = 1$, then we can plug this value into the equation $xy = -4$ to get $y = -4$. Therefore, the point $(1, -4)$ satisfies the equation.

x = 2

If $x = 2$, then we can plug this value into the equation $xy = -4$ to get $y = -2$. Therefore, the point $(2, -2)$ satisfies the equation.

x = -1

If $x = -1$, then we can plug this value into the equation $xy = -4$ to get $y = 4$. Therefore, the point $(-1, 4)$ satisfies the equation.

x = -2

If $x = -2$, then we can plug this value into the equation $xy = -4$ to get $y = 2$. Therefore, the point $(-2, 2)$ satisfies the equation.

Conclusion

In this article, we completed the coordinate table for the given equation $xy = -4$. We found the values of $x$ and $y$ that satisfy the equation and used the table to represent the relationship between the two variables. The equation represents a hyperbola, and the table helps us to visualize the curve and find the corresponding values of $x$ and $y$.

Final Answer

x	y
1	-4
2	-2
-1	4
-2	2

Step-by-Step Solution

1. Start by plugging in the values of $x$ into the equation $xy = -4$.
2. Solve for the value of $y$ using the equation $y = -\frac{4}{x}$.
3. Use the values of $x$ and $y$ to complete the coordinate table.
4. Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Tips and Tricks

• To complete the coordinate table, make sure to plug in the values of $x$ into the equation $xy = -4$ and solve for the value of $y$.
• Use the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Common Mistakes

• Make sure to plug in the values of $x$ into the equation $xy = -4$ and solve for the value of $y$.
• Use the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Real-World Applications

• The equation $xy = -4$ represents a hyperbola, which is a type of curve that has two branches.
• The coordinate table helps us to visualize the curve and find the corresponding values of $x$ and $y$.
• The equation $xy = -4$ can be used to model real-world situations, such as the motion of an object under the influence of gravity.

Future Directions

• The equation $xy = -4$ can be used to model more complex real-world situations, such as the motion of an object under the influence of multiple forces.
• The coordinate table can be used to visualize more complex curves, such as the graph of a polynomial function.
• The equation $xy = -4$ can be used to solve more complex problems, such as finding the maximum or minimum value of a function.
  

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Introduction

In our previous article, we completed the coordinate table for the given equation $xy = -4$. In this article, we will answer some frequently asked questions about completing the coordinate table for this equation.

Q: What is the equation $xy = -4$?

A: The equation $xy = -4$ represents a hyperbola, which is a type of curve that has two branches. The equation can be rewritten as $y = -\frac{4}{x}$, which represents a hyperbola with a horizontal asymptote at $y = 0$.

Q: How do I complete the coordinate table for the equation $xy = -4$?

A: To complete the coordinate table, you need to plug in the values of $x$ into the equation $xy = -4$ and solve for the value of $y$. You can use the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.

Q: What are the values of $x$ and $y$ that satisfy the equation $xy = -4$?

A: The values of $x$ and $y$ that satisfy the equation $xy = -4$ are $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$.

Q: How do I verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$?

A: To verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$, you need to plug in the values of $x$ and $y$ into the equation and check if the equation is true.

Q: What are some real-world applications of the equation $xy = -4$?

A: The equation $xy = -4$ can be used to model real-world situations, such as the motion of an object under the influence of gravity. It can also be used to model the behavior of a system with two variables.

Q: How can I use the equation $xy = -4$ to solve more complex problems?

A: The equation $xy = -4$ can be used to solve more complex problems, such as finding the maximum or minimum value of a function. It can also be used to model more complex real-world situations, such as the motion of an object under the influence of multiple forces.

Q: What are some common mistakes to avoid when completing the coordinate table for the equation $xy = -4$?

A: Some common mistakes to avoid when completing the coordinate table for the equation $xy = -4$ include:

• Not plugging in the values of $x$ into the equation $xy = -4$ and solving for the value of $y$.
• Not using the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Not verifying that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Q: What are some tips and tricks for completing the coordinate table for the equation $xy = -4$?

A: Some tips and tricks for completing the coordinate table for the equation $xy = -4$ include:

• Plugging in the values of $x$ into the equation $xy = -4$ and solving for the value of $y$.
• Using the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Verifying that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Conclusion

In this article, we answered some frequently asked questions about completing the coordinate table for the given equation $xy = -4$. We hope that this article has been helpful in understanding the equation and completing the coordinate table. If you have any further questions, please don't hesitate to ask.

Final Answer

x	y
1	-4
2	-2
-1	4
-2	2

Step-by-Step Solution

1. Start by plugging in the values of $x$ into the equation $xy = -4$.
2. Solve for the value of $y$ using the equation $y = -\frac{4}{x}$.
3. Use the values of $x$ and $y$ to complete the coordinate table.
4. Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Tips and Tricks

• To complete the coordinate table, make sure to plug in the values of $x$ into the equation $xy = -4$ and solve for the value of $y$.
• Use the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Common Mistakes

• Make sure to plug in the values of $x$ into the equation $xy = -4$ and solve for the value of $y$.
• Use the equation $y = -\frac{4}{x}$ to find the value of $y$ for each value of $x$.
• Verify that the points $(1, -4)$, $(2, -2)$, $(-1, 4)$, and $(-2, 2)$ satisfy the equation $xy = -4$.

Real-World Applications

• The equation $xy = -4$ represents a hyperbola, which is a type of curve that has two branches.
• The coordinate table helps us to visualize the curve and find the corresponding values of $x$ and $y$.
• The equation $xy = -4$ can be used to model real-world situations, such as the motion of an object under the influence of gravity.

Future Directions

• The equation $xy = -4$ can be used to model more complex real-world situations, such as the motion of an object under the influence of multiple forces.
• The coordinate table can be used to visualize more complex curves, such as the graph of a polynomial function.
• The equation $xy = -4$ can be used to solve more complex problems, such as finding the maximum or minimum value of a function.