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The table is asking to complete the values of \( y \) for the given function \( y = 2x + 1 \). The incomplete table has the following values:

| \( x \) | -1  |  0  |  1  |  2  |  3  |
|--------|------|------|------|------|------|
| \( y \) | -1  |  A  |  3  |  B  |  7  |

### Step-by-Step Solution:
The equation provided is \( y = 2x + 1 \). We'll calculate \( y \) for the corresponding \( x \)-values:

1. **When \( x = -1 \):**
   \[
   y = 2(-1) + 1 = -2 + 1 = -1
   \]
   This confirms the \( y \)-value for \( x = -1 \) is correct.

2. **When \( x = 0 \):**
   \[
   y = 2(0) + 1 = 0 + 1 = 1
   \]
   So, \( A = 1 \).

3. **When \( x = 1 \):**
   \[
   y = 2(1) + 1 = 2 + 1 = 3
   \]
   This confirms the \( y \)-value for \( x = 1 \) is correct.

4. **When \( x = 2 \):**
   \[
   y = 2(2) + 1 = 4 + 1 = 5
   \]
   So, \( B = 5 \).

5. **When \( x = 3 \):**
   \[
   y = 2(3) + 1 = 6 + 1 = 7
   \]
   This confirms the \( y \)-value for \( x = 3 \) is correct.

### Completed Table:

| \( x \) | -1  |  0  |  1  |  2  |  3  |
|--------|------|------|------|------|------|
| \( y \) | -1  |  1  |  3  |  5  |  7  |

Thus:
- \( A = 1 \)
- \( B = 5 \)

---

Would you like further clarification or a detailed explanation of any step? 

### Related Questions:
1. What does the slope of \( y = 2x + 1 \) represent in this context?
2. How would the graph of \( y = 2x + 1 \) look on a coordinate plane?
3. What happens to the \( y \)-values if we change the equation to \( y = 3x + 1 \)?
4. Can we derive the general formula for any linear equation \( y = mx + c \) from this problem?
5. How would the table change if \( x \) included negative numbers beyond -1 (e.g., -2, -3)?

### Tip:
In linear equations, \( m \) (slope) determines how steep the graph is, while \( c \) (intercept) determines where the graph crosses the \( y \)-axis.

Copy and complete the table below for the graph of y = 2x + 1. What values should replace A and B?

Learn how to solve and complete a table for the linear equation y = 2x + 1. Step-by-step explanation provided with calculations for each x-value, including A = 1 and B = 5. Suitable for Grade 6-8 students.

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