Let's go through the equations and check the tables for accuracy.

1. $y = 3x$

For this equation, we multiply the value of $x$ by 3 to get $y$.

• $x = 0$, $y = 3(0) = 0$
• $x = 1$, $y = 3(1) = 3$
• $x = 2$, $y = 3(2) = 6$

This table is correct.

2. $y = 2x$

Here, we multiply the value of $x$ by 2 to get $y$.

• $x = -2$, $y = 2(-2) = -4$ (The table has $y = -2$, so this is incorrect)
• $x = -1$, $y = 2(-1) = -2$ (Correct)
• $x = 0$, $y = 2(0) = 0$
• $x = 1$, $y = 2(1) = 2$
• $x = 2$, $y = 2(2) = 4$

So the first entry in the $y$-column should be corrected to $-4$.

3. $y = x + 3$

For this, we add 3 to each $x$-value to get $y$.

• $x = -3$, $y = (-3) + 3 = 0$
• $x = 0$, $y = 0 + 3 = 3$
• $x = 3$, $y = 3 + 3 = 6$
• $x = 6$, $y = 6 + 3 = 9$

The table is missing some values but seems correct for the provided $y$-values.

4. $y = 4x - 1$

Here, multiply $x$ by 4 and subtract 1.

• $x = 0$, $y = 4(0) - 1 = -1$
• $x = 1$, $y = 4(1) - 1 = 3$
• $x = 2$, $y = 4(2) - 1 = 7$
• $x = 3$, $y = 4(3) - 1 = 11$

There is a mistake in the table; for $x = 0$, $y$ should be $-1$.

5. $y = 2x + 5$

Here, multiply $x$ by 2 and add 5.

• $x = -2$, $y = 2(-2) + 5 = 1$
• $x = -1$, $y = 2(-1) + 5 = 3$
• $x = 0$, $y = 2(0) + 5 = 5$
• $x = 1$, $y = 2(1) + 5 = 7$
• $x = 2$, $y = 2(2) + 5 = 9$

The table has an incorrect entry for $x = -2$, as the correct value should be $y = 1$.

Summary of Corrections:

1. Problem 2: For $x = -2$, $y$ should be $-4$.
2. Problem 4: For $x = 0$, $y$ should be $-1$.
3. Problem 5: For $x = -2$, $y$ should be $1$.

Would you like more details or explanations on any of these?

Here are some follow-up questions you can consider:

1. What happens to the values of $y$ if we change the slope of the linear equations?
2. How would the equations change if we introduced negative slopes?
3. Can you graph these equations and observe the patterns they form?
4. How would you interpret the slope and intercept for each of these equations?
5. Can you find real-life examples where these linear equations might apply?

Tip: Always verify your table by substituting each $x$-value back into the equation to ensure the corresponding $y$-values are accurate.