The table provides values for $x$ and corresponding values for $y$. The task is to find which equation fits all pairs of values.

The pairs are:

• When $x = 1$, $y = 0$
• When $x = 2$, $y = -2$
• When $x = 3$, $y = -4$
• When $x = 4$, $y = -6$

We can observe that as $x$ increases by 1, $y$ decreases by 2. This indicates that the slope of the line is $-2$.

Now, let's check the provided options:

1. Option A: $y = -2x + 2$
   Substituting $x = 1$:
   $y = -2(1) + 2 = 0$, which is correct.
   Let's try $x = 2$:
   $y = -2(2) + 2 = -2$, correct again.
   Similarly, checking for $x = 3$ and $x = 4$ also satisfies the equation.
   So, this seems to be the correct equation.

2. Option B: $y = x - 1$
   For $x = 1$:
   $y = 1 - 1 = 0$, correct.
   But for $x = 2$:
   $y = 2 - 1 = 1$, which is incorrect.
   So, this is not the correct option.

3. Option C: $y = 2x - 2$
   For $x = 1$:
   $y = 2(1) - 2 = 0$, correct.
   But for $x = 2$:
   $y = 2(2) - 2 = 2$, which is incorrect.
   Hence, not the correct option.

4. Option D: $y = -2x - 1$
   For $x = 1$:
   $y = -2(1) - 1 = -3$, which is incorrect.
   So, this is not the correct option.

Conclusion: Option A ($y = -2x + 2$) is the correct answer.

Would you like further details or have any questions?

Related Questions:

1. How do we find the slope from a table of values?
2. Can this process be applied to non-linear equations?
3. What is the significance of the $y$-intercept in these equations?
4. How can we graphically verify this equation?
5. What happens when the slope is positive instead of negative?

Tip: Always verify your equation by substituting multiple points from the table to ensure accuracy.