Question

Tell whether x and y show direct variation. Explain your reasoning. y - x = 0

Answer 1

Y varies directly as x if y = kx for some constant, k.  In other words, y/x is constant.   y varies inversely as x if y = k/x for some constant, k.  In other words, xy is constant. The equation xy = 8 is an example of inverse variation, not direct variation.  

Answer 2

This is direct variation. If you move the x to the other side of the equation, it will become:
y = x

Direct variation is when y is equal to x times a constant. In this example, y is equal to 1 * x.