Final answer:
Equation a) y = 6x² is not an example of direct or inverse variation but a quadratic relationship, and b) x²y = 5 is an example of inverse variation when rewritten as y = 5/x².
Step-by-step explanation:
To determine if the given equations represent direct variation or inverse variation, we need to understand their forms. An equation of the form y = kx (where k is a constant) represents direct variation because the ratio of y to x is constant. An equation of the form xy = k or y = k/x represents inverse variation because the product of y and x is constant.
a) The equation y = 6x² is neither direct nor inverse variation. It represents a quadratic relationship where y is directly proportional to the square of x.
b) The equation x²y = 5 does represent an inverse variation. Rearranging it to y = 5/x², we can see that the product of x² and y is constant.