The equation y = \frac1x represents a hyperbola, a type of curve in mathematics. As x increases, y decreases, approaching zero but never touching it. This means that for larger values of x , the value of y becomes very small. When x is positive, y is also positive, and when x is negative, y is negative. The graph of this equation has two distinct branches, located in the first and third quadrants of the Cartesian plane. The line x = 0 is a vertical asymptote, meaning the curve never crosses it.