Direct Variation

Contributor: Jonathan Heagy. Lesson ID: 12676

If one potato at the store costs $1, and two potatoes cost $4, you'd be pretty confused! Somebody defied the law of direct variation! Or was bad at math! You'll be neither when you finish this lesson!


Middle School

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!


You walk into a grocery store to buy some avocados. Each one costs $1.25. How much would you expect to pay for 3 of them? 5 of them? None of them?

The concept you just used to figure those questions out is called "direct variation."

You expect that the avocados are priced the same no matter how many you buy. It would be ridiculous for one avocado to cost $1.25 and two avocados to cost $4. In order for direct variation to occur, three conditions must be reached:

  1. It takes the form y = (k)x, where k is called the "constant of variation."
  2. Our constant of variation is always the same.
  3. (0,0) is a solution to the equation.

Direct variation equations are super-easy to solve and can be graphed just like regular equations! A great example of this is the problem:

If y = 30 and x = 5, what is x when y = 72?

  1. First, we set up our direct variation equation: 30 = k(5).
  2. Dividing over the 5 means that k = 6, so we now can write y = 6x.
  3. We want to know x when y is 72, so we can set up the equation 72 = 6x.
  4. Dividing over the 6 gives us 12, so x = 12 when y = 72!
  • How does this relate to slope intercept form?
  • What does the constant of variation remind you of, and what is the y-intercept?

Try to think about why some equations are examples of direct variation and some are not!

Then, continue on to the Got It? section for a bit of a quiz!

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