Answer
inverse variation;
$xy=42$
Work Step by Step
Recall:
(1) A direct variation is represented by the equation $y=kx$ where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ also increases.
(2) An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ decreases.
Notice that in the given table, as the value of $x$ increases, the value of $y$ decreases.
This means that the table could involve an inverse variation.
Note further that for each pair of $x$ and $y$, the product of $x$ and $y$ is $42$.
Thus, the given table involves an inverse variation with $k=42$.
Therefore, the equation that models the inverse variation is $xy=42$.
