1. The problem asks to identify which graph corresponds to an equation of the form $y=\frac{k}{x}$, where $k$ is an integer. 2. The general form $y=\frac{k}{x}$ represents a reciprocal function, which is a hyperbola with two branches located in Quadrants I and III if $k>0$, or Quadrants II and IV if $k<0$. 3. Important characteristics of $y=\frac{k}{x}$: - Vertical asymptote at $x=0$. - Horizontal asymptote at $y=0$. - The graph is symmetric with respect to the origin. 4. Analyzing the given graphs: - Top-left graph: reciprocal hyperbola with branches in Quadrants I and III, asymptotes on the axes, passing near points $(1,2)$ and $(-1,-2)$. - Top-right graph: increasing cubic-like curve through the origin, not of the form $y=\frac{k}{x}$. - Bottom-left graph: exponential growth curve, not of the form $y=\frac{k}{x}$. - Bottom-right graph: upward-opening parabola, not of the form $y=\frac{k}{x}$. 5. Since the top-left graph matches the shape and properties of $y=\frac{k}{x}$, it is the correct choice. 6. To find $k$, use the point $(1,2)$: $$y=\frac{k}{x} \implies 2=\frac{k}{1} \implies k=2$$ Final answer: The equation graphed in the top-left graph is $y=\frac{2}{x}$, which is of the form $y=\frac{k}{x}$ with $k=2$.