WAEC Mathematics 2012 Paper

Concept:An inverse relationship means that when one variable increases, the other decreases proportionally.This relationship makes the product of the two variables a constant.Explanation:If $x$ and $y$ vary inversely, then $y$ is directly proportional to $\frac{1}{x}$.Using the constant $k$, we write:$$y = \frac{k}{x}$$Here, multiplying both sides by $x$ gives $xy = k$, which shows that the product is always the constant $k$.Now, examine the given options:Option A, $y = kx$, shows direct variation because $y$ increases as $x$ increases.Option C, $y = k\sqrt{x}$, is also a direct relationship involving a square root.Option D, $y = x + k$, is a linear addition, not inverse variation.Only Option B, $y = \frac{k}{x}$, correctly describes an inverse relationship.Answer:B. $y = \dfrac{k}{x}$