To determine which table has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of 2, let's examine each table in turn.
### Table (A)
[tex]\[
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
2 & 5 \\
6 & 15 \\
12 & 30 \\
\hline
\end{tabular}
\][/tex]
Check the ratios [tex]\( \frac{y}{x} \)[/tex]:
1. For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex]:
[tex]\[
\frac{5}{2} = 2.5
\][/tex]
2. For [tex]\( x = 6 \)[/tex], [tex]\( y = 15 \)[/tex]:
[tex]\[
\frac{15}{6} = 2.5
\][/tex]
3. For [tex]\( x = 12 \)[/tex], [tex]\( y = 30 \)[/tex]:
[tex]\[
\frac{30}{12} = 2.5
\][/tex]
Since the ratios are not equal to 2, Table (A) does not have a constant proportionality of 2.
### Table (B)
[tex]\[
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
3 & 6 \\
5 & 10 \\
18 & 36 \\
\hline
\end{tabular}
\][/tex]
Check the ratios [tex]\( \frac{y}{x} \)[/tex]:
1. For [tex]\( x = 3 \)[/tex], [tex]\( y = 6 \)[/tex]:
[tex]\[
\frac{6}{3} = 2
\][/tex]
2. For [tex]\( x = 5 \)[/tex], [tex]\( y = 10 \)[/tex]:
[tex]\[
\frac{10}{5} = 2
\][/tex]
3. For [tex]\( x = 18 \)[/tex], [tex]\( y = 36 \)[/tex]:
[tex]\[
\frac{36}{18} = 2
\][/tex]
Since all the ratios are equal to 2, Table (B) has a constant proportionality of 2.
### Table (C)
[tex]\[
\begin{tabular}{|ll|}
\hline
$x$ & $y$ \\
\hline
6 & 24 \\
10 & 40 \\
14 & 56 \\
\hline
\end{tabular}
\][/tex]
Check the ratios [tex]\( \frac{y}{x} \)[/tex]:
1. For [tex]\( x = 6 \)[/tex], [tex]\( y = 24 \)[/tex]:
[tex]\[
\frac{24}{6} = 4
\][/tex]
2. For [tex]\( x = 10 \)[/tex], [tex]\( y = 40 \)[/tex]:
[tex]\[
\frac{40}{10} = 4
\][/tex]
3. For [tex]\( x = 14 \)[/tex], [tex]\( y = 56 \)[/tex]:
[tex]\[
\frac{56}{14} = 4
\][/tex]
Since the ratios are not equal to 2, Table (C) does not have a constant proportionality of 2.
Therefore, the correct table with a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of 2 is:
[tex]\[
\boxed{B}
\][/tex]
