To determine which table represents a proportional relationship with a constant of proportionality [tex]\( k = 0.8 \)[/tex], we need to check if [tex]\( \frac{y}{x} = 0.8 \)[/tex] for the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values in each table.
### Table 1:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 4 & 8 & 10 \\
\hline
y & 0 & 0.5 & 1 & 1.25 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 4 \)[/tex]: [tex]\( \frac{y}{x} = \frac{0.5}{4} = 0.125 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( \frac{y}{x} = \frac{1}{8} = 0.125 \)[/tex]
- For [tex]\( x = 10 \)[/tex]: [tex]\( \frac{y}{x} = \frac{1.25}{10} = 0.125 \)[/tex]
None of these values equal [tex]\( 0.8 \)[/tex].
### Table 2:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 5 & 5 & 12.5 \\
\hline
y & 0 & 4 & 8 & 10 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( \frac{y}{x} = \frac{4}{5} = 0.8 \)[/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( \frac{y}{x} = \frac{8}{5} = 1.6 \)[/tex]
- For [tex]\( x = 12.5 \)[/tex]: [tex]\( \frac{y}{x} = \frac{10}{12.5} = 0.8 \)[/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is not consistently [tex]\( 0.8 \)[/tex].
### Table 3:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 4 & 8 & 10 \\
\hline
y & 0.8 & 0.8 & 0.8 & 0.8 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 4 \)[/tex]: [tex]\( \frac{y}{x} = \frac{0.8}{4} = 0.2 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( \frac{y}{x} = \frac{0.8}{8} = 0.1 \)[/tex]
- For [tex]\( x = 10 \)[/tex]: [tex]\( \frac{y}{x} = \frac{0.8}{10} = 0.08 \)[/tex]
None of these values equal [tex]\( 0.8 \)[/tex].
### Table 4:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 5 & 10 & 12.5 \\
\hline
y & 0.8 & 10.8 & 20.8 & 25.8 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( \frac{y}{x} = \frac{10.8}{5} = 2.16 \)[/tex]
- For [tex]\( x = 10 \)[/tex]: [tex]\( \frac{y}{x} = \frac{20.8}{10} = 2.08 \)[/tex]
- For [tex]\( x = 12.5 \)[/tex]: [tex]\( \frac{y}{x} = \frac{25.8}{12.5} = 2.064 \)[/tex]
None of these values equal [tex]\( 0.8 \)[/tex].
### Conclusion:
None of the tables given represent a proportional relationship with a constant of proportionality [tex]\( k = 0.8 \)[/tex].
