Directly Proportional

Pronunciation: /dɪˈrɛ prəˈpoʊr.ʃə.nl/ Explain

Two variables are directly proportional if they have a common ratio. This means that the dependent variable is a constant multiple of the independent variable.

The general formula for direct proportion is y = kx. In this formula k is called the constant of proportion or the constant of variation.

Sign advertising gasoline prices.
Figure 1: The price of gas.

Graph showing the relationship between gallons of gas and total price.
Figure 2: Graph showing the relationship between gallons of gas and total price.

An example of direct proportion is the price of gasoline. On a sign advertising the price of gas, the price is given in dollars per gallon, or price per liter. This price is the common ratio. To calculate the total cost, multiply the price per gallon or price per liter times the number of gallons or liters. If the price is $3.00 per gallon, the formula for the function is t(g) = 3g, where g is the number of gallon of gas and t(g) is the total cost of the gas.

A synonym for direct proportion is direct variation.

Click on the point on the blue slider and drag it to change the figure.

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


  1. McAdams, David E.. All Math Words Dictionary, directly proportional. 2nd Classroom edition 20150108-4799968. pg 62. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • McAdams, David E.. Direct Variation. Life is a Story Problem LLC. 1/23/2010.

Cite this article as:

McAdams, David E. Directly Proportional. 4/19/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

4/19/2019: Updated equations and expressions to the new format (McAdams, David E.)
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.)
6/7/2008: Corrected spelling. (McAdams, David E.)
3/10/2008: Correct grammar & formatting errors. Add verbiage (McAdams, David E.)
2/4/2008: Correct typo. (McAdams, David E.)
7/10/2007: Initial version. (McAdams, David E.)

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