Question

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

Answer 1

`-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!