To determine which table has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of 0.6, let's analyze each table step by step.
### Table (A)
[tex]\[
\left[\begin{array}{ll} x & y \\ 4 & 7 \\ 6 & 10 \\ 8 & 13 \end{array} \right]
\][/tex]
Calculate the proportionality constant [tex]\( k = \frac{y}{x} \)[/tex] for each pair of [tex]\( (x, y) \)[/tex]:
For [tex]\( x = 4, y = 7 \)[/tex]:
[tex]\[
k = \frac{7}{4} = 1.75
\][/tex]
For [tex]\( x = 6, y = 10 \)[/tex]:
[tex]\[
k = \frac{10}{6} \approx 1.67
\][/tex]
For [tex]\( x = 8, y = 13 \)[/tex]:
[tex]\[
k = \frac{13}{8} = 1.625
\][/tex]
The proportionality constants are approximately 1.75, 1.67, and 1.625. These are not all equal to 0.6.
### Table (B)
[tex]\[
\begin{tabular}{|ll|}
\hline $x$ & $y$ \\
\hline 4 & 2.4 \\
9 & 5.4 \\
14 & 8.4 \\
\hline
\end{tabular}
\][/tex]
Calculate the proportionality constant [tex]\( k = \frac{y}{x} \)[/tex] for each pair of [tex]\( (x, y) \)[/tex]:
For [tex]\( x = 4, y = 2.4 \)[/tex]:
[tex]\[
k = \frac{2.4}{4} = 0.6
\][/tex]
For [tex]\( x = 9, y = 5.4 \)[/tex]:
[tex]\[
k = \frac{5.4}{9} = 0.6
\][/tex]
For [tex]\( x = 14, y = 8.4 \)[/tex]:
[tex]\[
k = \frac{8.4}{14} = 0.6
\][/tex]
The proportionality constants are all equal to 0.6.
### Table (C)
[tex]\[
\begin{tabular}{|ll|}
\hline $x$ & $y$ \\
\hline 3 & 2 \\
9 & 6 \\
15 & 10 \\
\hline
\end{tabular}
\][/tex]
Calculate the proportionality constant [tex]\( k = \frac{y}{x} \)[/tex] for each pair of [tex]\( (x, y) \)[/tex]:
For [tex]\( x = 3, y = 2 \)[/tex]:
[tex]\[
k = \frac{2}{3} \approx 0.67
\][/tex]
For [tex]\( x = 9, y = 6 \)[/tex]:
[tex]\[
k = \frac{6}{9} = 0.67
\][/tex]
For [tex]\( x = 15, y = 10 \)[/tex]:
[tex]\[
k = \frac{10}{15} \approx 0.67
\][/tex]
The proportionality constants are all approximately 0.67, not 0.6.
### Conclusion
Only Table (B) has all proportionality constants equal to 0.6. Hence, the correct answer is:
[tex]\[
\boxed{\text{(B)}}
\][/tex]
