Is #x+y=6# a direct variation and if it is, how do you find the constant?

1 Answer
Oct 19, 2017

#x+y=6# is not a direct variation

Explanation:

There are several ways to see this:

  • a direct variation must be convertible into the form #y=cx# for some constant #c#; this equation can not be converted in this way.

  • #(x,y)=(0,0)# will always be a valid solution for a direct variation; it is not a solution for this equation. [Warning this is a necessary but not sufficient condition i.e. if #(x,y)=(0,0)# is a solution then the equation might or might not be a direct variation.]

  • if an equation is a direct variation and #(x,y)=(a,b)# is a solution, then for any constant #c#, #(x,y)=(cx,cy)# must also be a solution; in this case #(x,y)=(4,2)# is a solution but #(x,y)=(4xx3=12,2xx3=6)# is not a solution.