How do you determine the constant of variation for the direct variation given #-4y=8x+16#?

1 Answer
Oct 21, 2015

#-4y=8x+16# is not a direct variation

Explanation:

#-4y=8x# would be direct variation (with a constant of variation #= (-2)#
Doubling the value of #x# doubles the value of #y#
and the ratio #y/x = -2#
#color(white)("XXXXXX"){: (x,color(white)("XXX"),y,color(white)("XXX"), y/x), (1,color(white)("XXX"),-2,color(white)("XXX"),-2), (2,color(white)("XXX"),-4,color(white)("XXX"),-2), (3,color(white)("XXX"),-6,color(white)("XXX"),-2), (4,color(white)("XXX"),-8,color(white)("XXX"),-2) :}#

However
#-4y=8x+16# is not a direct variation
#color(white)("XXXXXX"){: (x,color(white)("XXX"),y,color(white)("XXX"), y/x), (1,color(white)("XXX"),-6,color(white)("XXX"),-6), (2,color(white)("XXX"),-8,color(white)("XXX"),-4), (3,color(white)("XXX"),-10,color(white)("XXX"),-3 1/3), (4,color(white)("XXX"),-12,color(white)("XXX"),-3) :}#
Note that the ratio #y/x# is not a constant in this case!