Answer
$B$
Work Step by Step
First, we need to find the constant of variation for this exercise. We are given an $x$ value and a $y$ value. Plug these values into the formula for direct variation, $y = kx$, to find $k$, the constant of variation:
$$10 = k(30)$$
Divide both sides by $30$ to isolate $k$:
$$k = \frac{10}{30}$$
Simplify the fraction by dividing both numerator and denominator by their greatest common factor, $10$:
$$k = \frac{1}{3}$$
The constant of variation is $\frac{1}{3}$.
Now, we want to find $y$ when $x$ is a specific value. Plug $y$ and $k$ into the formula for direct variation:
$$9 = \frac{1}{3}x$$
Divide each side of the equation by $\frac{1}{3}$, which means multiplying both sides by $3$, the reciprocal of $\frac{1}{3}$:
$$27 = x$$
This answer corresponds to option $B$.
