Is #x+y=6# a direct variation and if it is, how do you find the constant?
1 Answer
Oct 19, 2017
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.
