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Which table represents a proportional relationship with a constant of proportionality equal to 0.8?

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

GinnyAnswer
To determine which table represents a proportional relationship with a constant of proportionality equal to 0.8, we need to evaluate each table.

1. 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]

Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/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]

The constant of proportionality is 0.125, not 0.8.

2. Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0 & 4 & 8 & 10 \\ \hline \end{array} \][/tex]

Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 5\)[/tex], [tex]\(\frac{y}{x} = \frac{4}{5} = 0.8\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{8}{10} = 0.8\)[/tex]
- For [tex]\(x = 12.5\)[/tex], [tex]\(\frac{y}{x} = \frac{10}{12.5} = 0.8\)[/tex]

The constant of proportionality is indeed 0.8 for Table 2.

3. 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]

This table cannot represent a proportional relationship, as when [tex]\(x\)[/tex] changes, [tex]\(y\)[/tex] remains constant.

4. 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]

Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/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]

The constant of proportionality is not consistent and is not 0.8.

Therefore, the table that represents a proportional relationship with a constant of proportionality equal to 0.8 is:

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

So, the answer is Table 2.
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