Is ##8y=x## a direct variation, inverse variation, joint or neither?

The variation is direct.

##8color(red)(y=x## so, ## x = ky## Here ##color(red)(x,y) ## are variables and ##color(blue)(8## is the constant which is a fixed value for the variation.

Starting by assigning a set of values to ##y##

• Let ##y = 1 , x = (color(blue)(k).y ) = color(blue)(8) xx color(red)((1)) = 8##
• Let ##y = 2, x = color(blue)(8) xx color(red)((2)) = 16##
• Let ##y = 3, x = color(blue)(8)xx color(red)((3)) = 24##

Observing the trend in values of ##x## and ##y## we can conclude that the variation is direct because as one variable (##y##) increases so does the other variable(##x##).