Match the Equation to the Function Table: Identify the Correct Formula

To solve this problem, let's follow these steps:

• Identify key data points given in the problem.
• Determine if the data suggests a linear relationship.
• Calculate the slope using two points from the table.
• Calculate the y-intercept if necessary and match results with possible choices.

First, let's compute the slope $m$ using the first two points: $(-3, -1)$ and $(0, 0)$. The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{0 - (-3)} = \frac{1}{3}$

Next, we can check if any function $y = \frac{1}{3}x + b$ appears in the possible choices. Here since $(0, 0)$ is in the table, this suggests $b = 0$.

Thus, the equation becomes $y = \frac{1}{3}x$. This equation corresponds to choice 1. We can verify this by comparing with all given $X, Y$ pairs, and all satisfy the equation $y = \frac{1}{3} x$.

Therefore, the solution to the problem is $y = \frac{1}{3}x$.