Constant of Variation: Definition & Example

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Defining and Graphing Ellipses in Algebra

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 Definition
  • 0:43 Two Formats of…
  • 2:04 Finding the Constant…
  • 3:35 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

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.


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

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

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account