#-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!