Inverse variation
Inverse variation is a Grade 7 math skill from Yoshiwara Intermediate Algebra describing a relationship where y = k/x — as x increases, y decreases proportionally. The product xy is always the constant k, and the graph is a hyperbola.
Key Concepts
Property $y$ varies inversely with $x$ if.
$$y = \frac{k}{x}, x \neq 0$$.
where $k$ is a positive constant. This relationship implies that the product of the variables is constant: $xy = k$.
Common Questions
What is inverse variation?
Inverse variation is a relationship of the form y = k/x, where k is the constant of variation. As x increases, y decreases; the product xy = k is always constant.
How is inverse variation different from direct variation?
In direct variation y = kx, y increases as x increases. In inverse variation y = k/x, y decreases as x increases.
How do you find the constant of variation in inverse variation?
Multiply any corresponding x and y values: k = xy. The product is the same for all pairs in the table.
What does the graph of inverse variation look like?
The graph is a hyperbola with two branches in opposite quadrants, with asymptotes along both axes.