Function Table Selection: Identifying Y = X + 8 Relationship

To solve this problem, we need to determine the table that represents the function described by the equation $Y = X + 8$.

Let's examine each possible table choice:

• Choice 1: $\begin{array}{c|c} X & Y \\ \hline -1 & 7 \\ 2 & 10 \\ 5 & 15 \end{array}$ For $X = -1$, $Y = -1 + 8 = 7$ (correct), $X = 2$, $Y = 2 + 8 = 10$ (correct), $X = 5$, $Y = 5 + 8 == 13$. This does not satisfy for $X = 5$.
• Choice 2: $\begin{array}{c|c} X & Y \\ \hline 3 & -1 \\ 8 & -8 \\ 13 & -4 \end{array}$ This choice does not satisfy any of the pairings.
• Choice 3: $\begin{array}{c|c} X & Y \\ \hline -5 & 3 \\ 0 & 8 \\ 5 & 13 \end{array}$ Verify: $X = -5 \implies Y = -5 + 8 = 3$ (correct), $X = 0 \implies Y = 0 + 8 = 8$ (correct), $X = 5 \implies Y = 5 + 8 = 13$ (correct). All values satisfy $Y = X + 8$.
• Choice 4: $\begin{array}{c|c} X & Y \\ \hline 3 & 5 \\ 2 & 7 \\ 1 & 9 \end{array}$ This choice does not satisfy the equation for any pair.

Upon checking each table, Choice 3 is the only one that correctly matches the description of the function $Y = X + 8$ for all $X$ values shown.

Therefore, the solution is that the correct table is Choice 3.