Inverse variation describes a relationship between two variables where the product is constant. As one variable increases, the other decreases proportionally.
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In inverse variation, if $x$ and $y$ are variables, then $xy = k$, where $k$ is a non-zero constant.
The graph of an inverse variation is a hyperbola with asymptotes along the axes.
Inverse variation can be written in the form $y = \frac{k}{x}$.
As one variable approaches zero, the other variable approaches infinity, indicating an inverse proportionality.
If given data points for $x$ and $y$, you can determine if they represent an inverse variation by checking if their product is consistent.
Review Questions
What is the general form of an equation representing inverse variation?
How does the graph of an inverse variation look like?
How can you verify that two variables vary inversely using their values?
Related terms
Direct Variation: A relationship where as one variable increases, the other also increases proportionally. Represented by $y = kx$, where $k$ is a constant.
Constant of Variation: The constant value ($k$) in both direct and inverse variations which relates the variables in the equation.
Hyperbola: A type of curve on a graph that represents inverse variations; has two branches and asymptotes along its axes.