The Story Behind Direct Variation

A long time ago in the land of Algebra II, the wizard of magical numbers realized that he needed a great method to help his friends, the Dancing Gypsies of PI. When the Gypsies would try to dance a new move called “the wheel” they would trip all over each other’s feet due to the revolving line they would create. Seeing the greatest conflict of the world the wizard of magical numbers came to the conclusion that the Gypsies’ speed depends upon their distance of the center of rotation. Ultimately, the wizard saw that speed and distance are linked in some way and set out for an answer. After a few months locked away in his tower, he created Direct Variation for when the ratio of two variables is constant, the variables are direct. This means that if =a, for some nonzero constant a, then: y=ax. (The number a is the constant of variation and y is proportional to x). When the Wizard went to the gypsies to tell them of his new discovery another dance trend came in and the wizard did all that work for nothing! Too bad for him!!!

(Information given by the Wizard of Magical Numbers who is currently in a psych ward for schizophrenia)

How to use Direct Variation

The graph of y=3x is a line that passes through the origin (0,0). In a previous course you learned that the ratio gives the slope of a line. For a direct variation graph, the slope is just the constant of variation, a.

(Since the slope of the graph is or 3, the graph is y=3x)

You Are Doing Great!!!

Write an equation for the direct variation shown below:

The graph when looked closely at passes through the coordinates (-2, 3) so the constant of variation is:

A= = - 0r –1.5

An equation to the graph is y=-1.5x

Now that you have the idea let’s get some practice and go to some links!

http://school.discovery.com/quizzes/cc_dlaguens/53A.html

http://www.scs.nevada.edu/~roldant/MATH112/112VAR~1.HTM

http://www.mathnstuff.com/math/spoken/here/1words/v/v3.htm

http://www.purplemath.com/modules/variatn.htm

http://library.thinkquest.org/26342/sections/math_lessons/lessons/direction_variation.htm

http://www.scs.nevada.edu/~roldant/MATH112/112VAR~1.HTM

Sample Problems

Figure out the following graphs using the method that was previously shown.

Answer Key!!!!!!

First Graph shown: 3x+1

Second Graph shown: 1x

Third Graph Shown: 4x+3

The Creator

The Creator of this web page is a senior at Fayetteville High School located in Fayetteville, Arkansas. This web page was an assignment to give a way for more students to understand direct variation, despite how easy this area in Algebra II is. If anyone has any questions please email Jdaniel@fayar.net