1. We start with the equation of the graph to draw: $$2xy+1=0$$. 2. To understand the graph, we isolate $y$ in terms of $x$: $$2xy = -1 \implies y = \frac{-1}{2x}$$. 3. This equation describes a hyperbola with two branches, where $y$ is undefined at $x=0$ (vertical asymptote). 4. The graph has asymptotes along both the $x$-axis and $y$-axis because the product $xy$ is constant at $-\frac{1}{2}$. 5. Plotting this function will show two branches in the first and third quadrants or second and fourth quadrants depending on the sign; here $y = -\frac{1}{2x}$ changes sign accordingly.