How do you tell whether the equation x + 2y = 4 represents a direct variation. If so identify the constant?

1 Answer
Oct 6, 2015

#x+2y=4# is not a direct variation

Explanation:

Consider one possible simple solution for #x+2y=4#
#color(white)("XXX")x=2# and #y=1#

If the equation were a direct variation
multiplying #x# by any constant (for example #2#)
would result in a solution where #y# was multiplied by the same constant.

That is (using #2# as our constant
#color(white)("XXX")x=2*2#
would imply that
#color(white)("XXX")y=1*2 =2#

But evaluating #x+2y=4#
with #x=2# does not give #y=2#

Therefore the equation is not a direct variation