Direct Variation

Pronunciation: /dɪˈrɛkt ˌvɛər iˈeɪ ʃən/ ?

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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


  1. direct proportion. Encyclopedia Britannica. (Accessed: 2010-01-23). proportion.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 57-59. International Textbook Company, January 1963. (Accessed: 2010-01-12).
  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).

More Information

  • McAdams, David. Directly Proportional. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-23. Proportional.

Printed Resources

Cite this article as:

Direct Variation. 2010-01-23. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

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

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