Inverse Variation Formula

Inverse Variation Formula

A form of proportionality called inverse variation occurs when one number falls as the other rises, or the other way around. This suggests that if one number increases while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for the Inverse Variation Formula. The Inverse Variation Formula is represented by x=k/y.

Direct proportion means that as one quantity rises or falls, the other quantity also rises or falls. However, in indirect or inverse proportion, if one quantity rises, another falls, and vice versa.

An inverse relationship between two quantities is represented by inverse variation. Inverse variation has a variety of practical uses. For instance, the amount of time it takes to get there lowers as the speed of a car increases. The Inverse Variation Formula, graphs, and different instances are explained on the Extramarks’ website in-depth.

Some of the main points on the Inverse Variation Formula are:

1. When one quantity declines while another increases, and vice versa, both quantities are said to exhibit the Inverse Variation Formula.
2. When two quantities follow an Inverse Variation Formula, neither of them should be equal to 0, and their product must be a constant (constant of proportionality).
3. A rectangular hyperbola will appear in the cartesian coordinate plane when two quantities are followed by an Inverse Variation Formula.

What is Inverse Variation?

A proportionality between two quantities that have an inverse relationship is established through inverse variation. Two different proportionalities exist. Direct variation and inverse variation are these. If a rise or decrease in one quantity causes an equal increase or decrease in the other, the two quantities are said to be directly proportional to one another. With contrast, in an Inverse Variation Formula, one quantity grows while the other decreases.

The relationships between variables that are expressed in the form of y = k/x, where x and y are two variables and k is a constant number, are known as the Inverse Variation Formula. x=k/y is the Inverse Variation Formula.

According to this statement, if the value of one item rises, the value of the other quantity falls.

People notice in daily life that changes in one quantity’s values are influenced by changes in the values of other quantities. A variable is said to be inversely changing when compared to another variable. It illustrates how two quantities are inversely related to one another. As a result, one variable has an inverse relationship to another.

Inverse Variation Definition

A quantity is referred to as a variable if its value can fluctuate based on various circumstances. The link between two variables is known as an Inverse Variation Formula if a change in one variable’s value causes a change in the value of another related variable. A direct variation between two variables occurs when the value of one increases as the value of the other linked variable increases. The link between two variables is known as an Inverse Variation Formula if one variable’s value falls while another variable’s value rises or vice versa.

If the product of two non-zero numbers produces a constant term, then the quantities are said to be in an Inverse Variation Formula (constant of proportionality). In other words, if one quantity is directly proportional to the reciprocal of the other quantity, then the two quantities exhibit inverse variation. In other words, an increase in one quantity causes a decrease in the other, and vice versa for a drop in one quantity. In contrast to direct variation, when changes in one quantity cause changes in another immediately, in Inverse Variation Formula, the first quantity changes in the opposite direction of the other. Therefore, the relationship between the first and second quantities is inverse.

Inverse Variation Example

In daily lives, people encounter several examples of the Inverse Variation Formula in practice. For instance:

When a train travels a distance at a steady pace, the time required also grows, and vice versa.

When more individuals are involved in a task, it takes less time to complete it.

Let’s say that x and y exhibit inverse variation. Given are the values of x = 10 and the proportionality constant, 50. Then, y will have a value of 50 / 10 = 5.

Inverse Variation Formula

Proportionality is denoted by the symbol ” “. Two quantities, x and y, are expressed as follows if they exhibit Inverse Variation Formula:

x ∝ 1/y

y ∝ 1/x

A constant or coefficient of proportionality must be added in order to turn this expression into an equation. As a result, the following is the formula for inverse variation:

x = k /y, or y = k /x,

The proportionality constant in this case is k. Additionally, x 0 and y 0

The variables x and y are represented by the following formula, if any variable x is inversely proportional to another variable y according to the Inverse Variation Formula:

y=k/x or xy=k

where any value for k is a constant.

Inverse Variation Graph

In an inverse variation, the inverse percentage establishes the link between two quantities or variables. The inverse relationship between two quantities, x and y, is provided by:

x ∝ 1/y

To determine the connection between two quantities in inverse variation, look at the examples provided below.

An Inverse Variation Formula’s graph looks like a rectangular hyperbola. When two quantities x and y are under inverse variation, the sum of the two values equals a fixed number k. Since neither x nor y may equal zero, the graph can never cross either axis.

Inverse Variation Table

To analyse how one quantity changes in response to a change in another quantity that follows an inverse proportionality, use an inverse variation table. Assume that y = 18 / x describes the inverse variation of two values, x and y. So, the following is the inverse variation table:

x y = 18 / x

1 18

2 9

3 6

-3 -6

-2 -9

-1 -18

Examples on Inverse Variation

1. How long will it take 10 people to finish the same task if 12 workers finish it in 5 hours?

Solution: Let x represent the workforce and y represent the project’s completion time. If there are fewer workers, it will take longer to do the work. An Inverse Variation Formula is thus present in this instance. By applying the product rule,

x1/x2= y2/y1

y = 6 hrs.

The task will take 10 workers 6 hours to complete.

2 Identify the proportionality constant if x = 12 and y = 4 display inverse variance.

Solution: Due to the Inverse Variation Formula between x and y, xy = k (12)(4) = 48 = k.

k = 48 is the proportionality constant.

3. What will the value of x be when x and y are in inverse variation if the proportionality constant is 7 and y is equal to 14?

Solution: Due to the inverse relationship between x and y, xy = k x = k / y x = 7 / 14 = 0.5.

The answer is x = 1/2, or 0.5

Practice Questions on Inverse Variation

The Extramarks website is dedicated to fostering academic excellence by safeguarding student success and development. On the Extramarks website, students can obtain the practice questions on Inverse Variation. This “online learning platform” is used as an illustration to show how technology could boost education’s efficacy. To aid students in properly grasping the topics, the Extramarks website provides chapter-based worksheets, interactive exercises, an infinite number of practice questions, and more. With adaptive quizzes that include progressively more challenging difficulty levels, MCQs, and mock exams so that they can create an upward learning graph, students can assess their knowledge. The subject matter specialists at Extramarks prepared the practice questions for the students in order to help students fully grasp the concepts. On the basis of a strong foundation, students will learn complex topics in later chapters and in higher grades.

1. How can students determine whether something is an inverse variation?

In Mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.

2. How can students use inverse variation in their day-to-day life?

For instance, when travelling to a specific area, the amount of time it takes to get there lowers as the speed rises. The amount of time it takes to get there grows as the speed decreases. The amounts are therefore inversely proportional.

3. Why do students need to learn about inverse variation?

When learning equations and understanding graphs, it is crucial to comprehend the concepts of inverse variation and direct variation. Inverse relationships are crucial, not just in Mathematics but particularly in Physics.