Compare the graphs of the inverse variations? Please provide 3 comparisons. Y=-0.2\x and y=-0.3\x

See

http://www.wolframalpha.com/input/?i=plot+y+%3D+-.2%2Fx,+y+%3D+-.3%2Fx

To compare the graphs of inverse variations, we can start by understanding the general characteristics of inverse variation graphs. Inverse variation occurs when one variable increases while the other variable decreases, and their product remains constant. The equation of an inverse variation can be written in the form y = k/x, where k is the constant of variation.

Now, let's compare the graphs of the inverse variations y = -0.2/x and y = -0.3/x:

1. Constant of Variation (k):
- In the first equation y = -0.2/x, the constant of variation is -0.2.
- In the second equation y = -0.3/x, the constant of variation is -0.3.

2. Slope:
- In inverse variation graphs, the slope is the result of the constant of variation.
- As the constant of variation for the second equation (-0.3) is greater than that of the first equation (-0.2), the second graph will have a steeper slope compared to the first graph.

3. Asymptotes:
- In inverse variation graphs, there is an asymptote, which is a line that the graph approaches but never crosses.
- The vertical asymptote occurs at x = 0, as division by zero is undefined. Thus, both graphs will have a vertical asymptote at x = 0.
- The horizontal asymptote occurs at y = 0. As x approaches infinity or negative infinity, the value of y approaches zero. Therefore, both graphs will have a horizontal asymptote at y = 0.

In summary, the three comparisons between the graphs of y = -0.2/x and y = -0.3/x are:
1. The constant of variation: -0.3 for y = -0.3/x and -0.2 for y = -0.2/x.
2. The slope: The second graph (y = -0.3/x) will have a steeper slope due to a larger constant of variation.
3. The asymptotes: Both graphs have a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.