Inverse variation describes a relationship where the product of two variables is constant. When one variable increases, the other decreases proportionally.
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The general form of an inverse variation equation is $xy = k$, where $k$ is a non-zero constant.
If $y$ varies inversely as $x$, then $y = \frac{k}{x}$ for some constant $k$.
Graphically, inverse variation forms a hyperbola on a coordinate plane.
$k$ must always be non-zero; if $k=0$, the relationship is not considered an inverse variation.
In practical terms, inverse variations often model situations where increasing one quantity results in the decrease of another, such as speed and travel time.
Review Questions
What is the general form of an inverse variation equation?
How does the graph of an inverse variation appear on a coordinate plane?
What happens to one variable when the other increases in an inverse variation?
Related terms
Direct Variation: A relationship between two variables in which they increase or decrease together at a constant rate, typically expressed as $y = kx$.
Constant of Proportionality: The constant value ($k$) that relates two variables in either direct or inverse variation.
Hyperbola: A type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. Inverse variations graph into hyperbolas.