Is #7x+4y=2# a direct variation equation and if so, what is the constant of variation?

1 Answer
Dec 8, 2015

It is a direct variation is you can rewrite it in the form #y=m*x# where #m# is the constant.

Explanation:

We first bring the #y#'s to one side and the rest to the other, by subtracting #7x# from both sides:
#4y=-7x+2#

Then divide both sides by 4:
#y=-7/4x+1/2#

This is a linear equation, but according to my definition, this is not a direct variation, as there is allways this constant #1/2#. The graph of a direct variation should go through the origin:
graph{7/4x+1/2 [-10, 10, -5, 5]}