Final answer:
The equation y = -(3)/(x) describes a hyperbola, which is a curve showing an inverse relationship between x and y, differing from linear equations such as y = 9 + 3x. It is undefined at the origin as division by zero is undefined, and sketching this on a graph shows a distinct curve.
Step-by-step explanation:
The equation y = -(3)/(x) is a representation of a hyperbolic function, showing an inverse relationship between variables x and y. Unlike linear equations of the form y = b + mx, this equation describes a curve where y decreases as x increases, and is undefined at x = 0. In the context of graphing, if you were to plot both y = -(3)/(x) and a linear equation like y = 9 + 3x, you would see distinct differences between the shapes of the graph.
The point where both x and y are zero (origin) is a point of contention in this relationship because division by zero is undefined, leading to a break in the graph of y = -(3)/(x). To understand the behavior of the hyperbola, you can see how as x approaches zero from either direction, y tends to increase or decrease without bound, which is often represented as y approaching infinity (y → ∞).
On a graph, sketching the function y = -(3)/(x) would result in a curve that is closer to the axes near the origin and gradually moves away as x moves further from zero. For transformation or comparison, graphing additional functions such as y = x, y = (x - 2)^2, y = e^x, and y = -e^x on the same diagram can be useful in visualizing different types of relationships between x and y.