Does x y3 show direct variation?

To determine if ( xy^3 ) shows direct variation, we check if it can be expressed in the form ( y = kx ), where ( k ) is a constant. In the case of ( xy^3 ), it is more appropriate to analyze it as a function of ( y ): if we isolate ( y ), we find ( y^3 = \frac{k}{x} ), indicating that ( y ) varies inversely with ( x ). Therefore, ( xy^3 ) does not show direct variation.