The task involves matching each table of data with its corresponding equation on the right and briefly explaining why they match.

Here are the steps to approach this:

1. Analyze the Tables:

Each table shows a set of $x$ and $y$ values. We need to determine the relationship between the variables, which should match one of the equations given on the right-hand side.

2. Equations on the Right:

The possible equations are:

1. $y = x$
2. $y = 3x - 1$
3. $y = x + 3$
4. $y = x^2$
5. $y = -x^2$
6. $y = x^2 + 3$

3. Match the Data from Each Table:

Table A:

• $x = 1, 2, 0, -1, -2$
• $y = 4, 7, 3, 0, -2$

Let’s check the equation $y = 3x - 1$:

• For $x = 1$, $y = 3(1) - 1 = 2$, but the actual value is $y = 4$, so this doesn't match. Try $y = x + 3$:
• For $x = 1$, $y = 1 + 3 = 4$
• For $x = 2$, $y = 2 + 3 = 5$ (Does not match exactly with table A either).

I will calculate carefully based on patterns, then match with best