Answer
$y=10$
Work Step by Step
Recall:
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.
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 $(x, y)$ then substituting the values of $x$ and $y$ into the direct variation formula $y=kx$.
Since the variation contains the point $(2, 5)$, substitute these into the formula $y=kx$ to obtain:
\begin{align*}
y&=kx\\\\
5&=k(2)\\\\
\frac{5}{2}&=k\\\\
2.5&=k\end{align*}
Therefore, the equation that models the direct variation is $y=2.5x$.
To find the value of $y$ when $x=4$, substitute $4$ to $x$ in the equation above to obtain:
\begin{align*}
y&=2.5x\\\\
y&=2.5(4)\\\\
y&=10\\\\
\end{align*}
