Answer
direct variation;
$y=2x$
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 $y$ also increases.
This means that the table could involve a direct variation.
Note further that for each value of $x$, the value of $y$ can be found by multiplying $2$ to the value of $x$.
Thus, the given table involves a direct variation.
The equation that models the direct variation can be determined by solving the value of $k$:
This can be done by taking any ordered pair from the table, then substituting the values of $x$ and $y$ into the direct variation formula $y=kx$.
Using $(11, 22)$:
\begin{align*}
y&=kx\\\\
22&=k(11)\\\\
\frac{22}{11}&=\frac{k(11)}{11}\\\\
2&=k
\end{align*}
Therefore, the equation that models the direct variation is $y=2x$.
