Direct Variation

Pronunciation: /dɪˈrɛkt ˌvɛər iˈeɪ ʃən/ ?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 1: Direct variation.

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

References

  1. direct proportion. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-23). http://www.merriam-webster.com/dictionary/direct proportion.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 57-59. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n74/mode/1up/search/variation.
  3. Young, J. W. A. and Jackson, Lambert L.. A First Course in Elementary Algebra, pp 167-174. D. Appleton and Company, 1910. (Accessed: 2010-01-23). http://www.archive.org/stream/firstcourseinele00younrich#page/167/mode/1up/search/direct+variation.

More Information

  • McAdams, David. Directly Proportional. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-23. http://www.allmathwords.org/article.aspx?lang=en&id=Directly Proportional.

Printed Resources

Cite this article as:


Direct Variation. 2010-01-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/directvariation.html.

Translations

Image Credits

Revision History


2010-01-23: Added "References" (McAdams, David.)
2008-07-11: Added manipulative (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License