Direct Variation

Pronunciation: /dɪˈrɛkt ˌvɛər.iˈeɪ.ʃən/ Explain

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Which value of the constant of variation would indicate a gas price of $3.00 per gallon?
Manipulative 1 - Direct Variation Created with GeoGebra.

Direct variation means the output varies from the input by a ratio.[1] The general form of the equation for direct variation y = mx where m is the constant of variation.

An example of direct variation is buying gas. When you pump the gas, the total price varies directly as a function of the number of gallons of gas you pump. The constant of variation is the price per gallon. So, if gas costs $2.50 per gallon, the equation is y = $2.50x where x is the number of gallons pumped and y is the total price. If you pump 10 gallons of gas, the price is $25.00.

Note that direct variation always has a y-intercept of zero. The graph of the direct variation above looks likes this:
Graph of direct variation


  1. McAdams, David E.. All Math Words Dictionary, direct variation. 2nd Classroom edition 20150108-4799968. pg 61. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. direct proportion. Encyclopedia Britannica. Merriam-Webster. Last Accessed 7/3/2018. proportion. Buy the book
  3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 57-59. International Textbook Company. January 1963. Last Accessed 7/3/2018. Buy the book
  4. Young, J. W. A. and Jackson, Lambert L.. A First Course in Elementary Algebra. pp 167-174. D. Appleton and Company. 1910. Last Accessed 7/3/2018. Buy the book

More Information

  • McAdams, David E.. Directly Proportional. All Math Words Encyclopedia. Life is a Story Problem LLC. 1/23/2010.

Cite this article as:

McAdams, David E. Direct Variation. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/23/2010: Added "References". (McAdams, David E.)
7/11/2008: Added manipulative. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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