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Constant of Variation: Definition & Example

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  • 0:04 Definition
  • 0:43 Two Formats of…
  • 2:04 Finding the Constant…
  • 3:35 Lesson Summary
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Lesson Transcript
Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

In this lesson, you will learn the definition of constant of variation and how it relates to variables. You will learn the different formats of equations that are helpful in identifying the constant of variation in equations.

Definition

At first glance, the term 'constant of variation' might seem like a contradiction. After all, 'constant' means to stay the same, while 'variation' refers to change. But as you will soon see, they make sense together in the world of math. In math, variation shows how one variable changes in relation to another variable. This relationship is usually expressed as a ratio. When we say that the variation is constant, we are saying that that ratio remains the same. So when you see the term constant of variation, just remember that it means the relationship between the variables does not change.

Two Formats of Variation Problems

Variation problems are normally seen in one of two formats. In both cases, k represents the constant of variation. If an equation can be written in either of these formats, you can identify the constant of variation.

k = xy

k = y/x

Keep in mind that not all equations can be written this way, so not every equation will have a constant of variation.

The first equation represents inverse variation, and the second equation represents direct variation. If we were to graph an equation that is direct variation, we would see that it is a straight line. The constant of variation would be the rate of change, which has the same value as the slope. For example, this graph shows the distance traveled over a period of time. The equation for this linear pattern can be represented by y = 3.5x or 3.5 = y/x. In this case, the number 3.5 is the constant of variation and tells us the rate of change in meters per second.

Graph showing constant of variation as a rate of change
graph

This concept can also be seen in science. For instance, in chemistry, it's important to find the equilibrium constant of a chemical reaction. The equilibrium constant shows the ratio of the concentrations of products and reactants in a reaction.

Finding the Constant of Variation

Now let's look at a few examples.

Example 1:

y/x = -12

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