Inversely Proportional

Pronunciation: /ɪnˈvɜr'sli prəˈpoʊr.ʃə.nl/ Explain

Two variables are inversely proportional if the multiplicative inverse of one has a common ratio with the other. A general equation for variables that are inversely proportional is
.
In this equation x and y are the variables that are inversely proportional. a is the constant of variation.

An example of variables that are inversely proportional is the time it takes to make a trip as a function of speed. The faster you go, the quicker (less time) you get there. This can be expressed with the function

where t(s) is the time it takes to make the trip, 100 is the distance, and s is the speed of travel.

References

1. McAdams, David E.. All Math Words Dictionary, inversely proportional. 2nd Classroom edition 20150108-4799968. pg 102. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. inversely proportional. merriam-webster.com. Merriam-Webster Online Dictionary. Merriam-Webster. 2010. Last Accessed 8/7/2018. http://www.merriam-webster.com/dictionary/inversely%20proportional. Buy the book
3. Davies, Charles. New Elementary Algebra : Embracing the First Principles of the Science. pp 274-275. www.archive.org. Barnes & Burr, Publishers. 1864. Last Accessed 8/7/2018. http://www.archive.org/stream/newelementaryalg00daviiala#page/274/mode/1up/search/inversely. Buy the book
4. Underwood,Ralph S.; Nelson,Thomas R.; Selby,Samuel.. Intermediate Algebra. pp 218-219. www.archive.org. The Macmillan Company. 1947. Last Accessed 8/7/2018. http://www.archive.org/stream/intermediatealge033585mbp#page/n219/mode/1up/search/inversely. Buy the book
5. Rong Yang. A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1. revised edition. pg 269. A-Plus Notes Learning Center. January 1, 2006. Last Accessed 8/7/2018. Buy the book

More Information

• McAdams, David E.. Proportional. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/p/proportional.html.

Cite this article as:

McAdams, David E. Inversely Proportional. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/i/inverselyproportional.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/2/2010: Added "References". (McAdams, David E.)
8/13/2008: Added general equation for inverse proportion. Changed equation t(s)=100/s to hot_eqn. Added vocabulary link for 'multiplicative inverse' (McAdams, David E.)
7/7/2008: Corrected link errors. Corrected spelling (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)