a direct variation function contains the points (-9, -3) and (-12, -4). which equation represents the…

Explanation:

Step1: Recall direct - variation formula

The formula for a direct - variation function is $y = kx$, where $k$ is the constant of variation.

Step2: Find the value of $k$ using a point

Using the point $(-9,-3)$, substitute $x=-9$ and $y = - 3$ into $y=kx$. We get $-3=k\times(-9)$. Solving for $k$, we have $k=\frac{-3}{-9}=\frac{1}{3}$.

Step3: Write the equation of the function

Since $k = \frac{1}{3}$, the equation of the direct - variation function is $y=\frac{1}{3}x$.

Answer:

C. $y=\frac{x}{3}$