To determine which table has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of 4, we need to check the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values in the table. The table where this ratio is consistently 4 will have a constant of proportionality of 4.
Let's go through each table step-by-step.
Table (A):
[tex]\[
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
4 & 16 \\
9 & 36 \\
16 & 64 \\
\hline
\end{tabular}
\][/tex]
Calculate the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
1. For [tex]\( x = 4 \)[/tex], [tex]\( y = 16 \)[/tex]:
[tex]\[
\frac{16}{4} = 4
\][/tex]
2. For [tex]\( x = 9 \)[/tex], [tex]\( y = 36 \)[/tex]:
[tex]\[
\frac{36}{9} = 4
\][/tex]
3. For [tex]\( x = 16 \)[/tex], [tex]\( y = 64 \)[/tex]:
[tex]\[
\frac{64}{16} = 4
\][/tex]
Since all three ratios give us 4, Table (A) has a constant of proportionality of 4.
Table (B):
[tex]\[
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
2 & 8 \\
10 & 16 \\
15 & 21 \\
\hline
\end{tabular}
\][/tex]
Calculate the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
1. For [tex]\( x = 2 \)[/tex], [tex]\( y = 8 \)[/tex]:
[tex]\[
\frac{8}{2} = 4
\][/tex]
2. For [tex]\( x = 10 \)[/tex], [tex]\( y = 16 \)[/tex]:
[tex]\[
\frac{16}{10} = 1.6
\][/tex]
3. For [tex]\( x = 15 \)[/tex], [tex]\( y = 21 \)[/tex]:
[tex]\[
\frac{21}{15} = 1.4
\][/tex]
Since the ratios are not all the same and not all equal to 4, Table (B) does not have a constant of proportionality of 4.
Table (C):
[tex]\[
\left\lvert\,
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
3 & 12 \\
5 & 18 \\
11 & 36 \\
\hline
\end{tabular}\right.
\][/tex]
Calculate the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
1. For [tex]\( x = 3 \)[/tex], [tex]\( y = 12 \)[/tex]:
[tex]\[
\frac{12}{3} = 4
\][/tex]
2. For [tex]\( x = 5 \)[/tex], [tex]\( y = 18 \)[/tex]:
[tex]\[
\frac{18}{5} = 3.6
\][/tex]
3. For [tex]\( x = 11 \)[/tex], [tex]\( y = 36 \)[/tex]:
[tex]\[
\frac{36}{11} \approx 3.27
\][/tex]
Since the ratios are not all the same and not all equal to 4, Table (C) does not have a constant of proportionality of 4.
Conclusion:
Only Table (A) has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of 4.
Therefore, the answer is:
[tex]\[
\boxed{1}
\][/tex]
