Answer
When $y = 9$, then $x = 27$.
Work Step by Step
A direct variation is represented by the equation $y = kx$ where $k$ is the constant of variation.
Since $y = 10$ when $x = 30$, substitute these values into $y=kx$ to find the value of $k$:
$y=kx\\
10 = k(30)$
Divide both sides by $30$ to solve for $k$:
$k = \frac{10}{30}$
$k = \frac{1}{3}$
Thus, the direct variation is represented by the equation $y=\frac{1}{3}x$.
Substitute $y=9$ into the equation above to find the corresponding value of $x$:
$y=\frac{1}{3}x\\
9 = \frac{1}{3}(x)$
Multiply $3$ to both sides to obtain:
$3(9) = 3\left(\frac{1}{3}(x)\right)$
27=x$
Thus, when $y = 9$, then $x = 27$.
