Not substituting the given values of x and y into the equation

Oct 13, 2025 by pynkocean.com 51 views

Inverse Variation: Understanding the Relationship between x and y

What is Inverse Variation?

Inverse variation is a type of mathematical relationship between two variables, x and y, where the product of the two variables remains constant. In other words, as one variable increases, the other variable decreases, and vice versa. This type of variation is often represented by the equation y = k/x, where k is a constant.

Given Information

We are given that when x = 4.5, y = 3. This information will help us write an inverse variation equation that shows the relationship between x and y.

Writing the Inverse Variation Equation

To write the inverse variation equation, we need to find the value of the constant k. We can do this by substituting the given values of x and y into the equation y = k/x.

y = k/x 3 = k/4.5

To solve for k, we can multiply both sides of the equation by 4.5.

k = 3 × 4.5 k = 13.5

Now that we have found the value of k, we can write the inverse variation equation.

y = 13.5/x

Understanding the Equation

The equation y = 13.5/x represents the relationship between x and y. As x increases, y decreases, and vice versa. This means that if we know the value of x, we can use the equation to find the corresponding value of y.

Example

Let's say we want to find the value of y when x = 2. We can substitute x = 2 into the equation y = 13.5/x.

y = 13.5/2 y = 6.75

Therefore, when x = 2, y = 6.75.

Graphing the Equation

The graph of an inverse variation equation is a hyperbola, which is a type of curve that approaches the x-axis and y-axis but never touches them. The graph of the equation y = 13.5/x is a hyperbola that opens in the first and third quadrants.

Real-World Applications

Inverse variation has many real-world applications, including:

Physics: Inverse variation is used to describe the relationship between the distance of an object from a source of light and the intensity of the light.
Economics: Inverse variation is used to describe the relationship between the price of a product and the quantity demanded.
Biology: Inverse variation is used to describe the relationship between the concentration of a substance and the rate of reaction.

Conclusion

In this article, we have learned about inverse variation and how to write an inverse variation equation. We have also seen how to use the equation to find the value of y when x is given. Inverse variation has many real-world applications, and understanding this concept is essential for solving problems in physics, economics, and biology.

Key Takeaways

Inverse variation is a type of mathematical relationship between two variables, x and y.
The equation y = k/x represents the relationship between x and y.
The value of k is a constant that can be found by substituting the given values of x and y into the equation.
Inverse variation has many real-world applications, including physics, economics, and biology.

Frequently Asked Questions

What is inverse variation? Inverse variation is a type of mathematical relationship between two variables, x and y, where the product of the two variables remains constant.
How do I write an inverse variation equation? To write an inverse variation equation, you need to find the value of the constant k by substituting the given values of x and y into the equation y = k/x.
What are some real-world applications of inverse variation? Inverse variation has many real-world applications, including physics, economics, and biology.
Inverse Variation Q&A: Frequently Asked Questions

Introduction

Inverse variation is a fundamental concept in mathematics that describes the relationship between two variables, x and y. In this article, we will answer some of the most frequently asked questions about inverse variation, including how to write an inverse variation equation, how to use the equation to solve problems, and what are some real-world applications of inverse variation.

Q: What is inverse variation?

A: Inverse variation is a type of mathematical relationship between two variables, x and y, where the product of the two variables remains constant. This means that as one variable increases, the other variable decreases, and vice versa.

Q: How do I write an inverse variation equation?

A: To write an inverse variation equation, you need to find the value of the constant k by substituting the given values of x and y into the equation y = k/x. For example, if we are given that when x = 4.5, y = 3, we can substitute these values into the equation to find the value of k.

y = k/x 3 = k/4.5

To solve for k, we can multiply both sides of the equation by 4.5.

k = 3 × 4.5 k = 13.5

Now that we have found the value of k, we can write the inverse variation equation.

y = 13.5/x

Q: How do I use the inverse variation equation to solve problems?

A: To use the inverse variation equation to solve problems, you need to substitute the given values of x and y into the equation and solve for the unknown variable. For example, if we are given that x = 2 and y = 6.75, we can substitute these values into the equation to find the value of k.

y = k/x 6.75 = k/2

To solve for k, we can multiply both sides of the equation by 2.

k = 6.75 × 2 k = 13.5

Now that we have found the value of k, we can write the inverse variation equation.

y = 13.5/x

Q: What are some real-world applications of inverse variation?

A: Inverse variation has many real-world applications, including:

Physics: Inverse variation is used to describe the relationship between the distance of an object from a source of light and the intensity of the light.
Economics: Inverse variation is used to describe the relationship between the price of a product and the quantity demanded.
Biology: Inverse variation is used to describe the relationship between the concentration of a substance and the rate of reaction.

Q: How do I graph an inverse variation equation?

A: The graph of an inverse variation equation is a hyperbola, which is a type of curve that approaches the x-axis and y-axis but never touches them. To graph an inverse variation equation, you need to plot the points (x, y) and draw a smooth curve through them.

Q: What are some common mistakes to avoid when working with inverse variation?

A: Some common mistakes to avoid when working with inverse variation include:

Not substituting the given values of x and y into the equation: Make sure to substitute the given values of x and y into the equation to find the value of k.
Not solving for k: Make sure to solve for k by multiplying both sides of the equation by the value of x.
Not using the correct equation: Make sure to use the correct equation, which is y = k/x.

Q: How do I check my work when working with inverse variation?

A: To check your work when working with inverse variation, you need to substitute the values of x and y into the equation and make sure that the equation is true. For example, if we are given that x = 4.5 and y = 3, we can substitute these values into the equation to check our work.

y = k/x 3 = k/4.5

To solve for k, we can multiply both sides of the equation by 4.5.

k = 3 × 4.5 k = 13.5

Now that we have found the value of k, we can write the inverse variation equation.

y = 13.5/x

We can substitute the values of x and y into the equation to check our work.

y = 13.5/x 3 = 13.5/4.5

To solve for y, we can multiply both sides of the equation by 4.5.

y = 13.5/4.5 × 4.5 y = 3

Therefore, our work is correct.

Conclusion

Inverse variation is a fundamental concept in mathematics that describes the relationship between two variables, x and y. In this article, we have answered some of the most frequently asked questions about inverse variation, including how to write an inverse variation equation, how to use the equation to solve problems, and what are some real-world applications of inverse variation. We hope that this article has been helpful in understanding inverse variation and how to use it to solve problems.