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Which table represents a proportional relationship that has a constant of proportionality equal to [tex]$0.8$[/tex]?

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 4 & 8 & 10 \\
\hline
$y$ & 0 & 0.5 & 1 & 1.25 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 5 & 5 & 12.5 \\
\hline
$y$ & 0 & 4 & 8 & 10 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 4 & 8 & 10 \\
\hline
$y$ & 0.8 & 0.8 & 0.8 & 0.8 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 5 & 10 & 12.5 \\
\hline
$y$ & 0.8 & 10.8 & 20.8 & 25.8 \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
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].
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