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

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:

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.