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Use the table to find the relationship between the two quantities.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
1 & 13 \\
\hline
2 & 26 \\
\hline
3 & 39 \\
\hline
4 & 52 \\
\hline
\end{tabular}

What relationship between the quantities is shown in the table?

A. The relationship between quantities is +12.
B. The relationship between quantities is [tex]$\times 13$[/tex].
C. The relationship between quantities is -24.
D. The relationship between quantities is +36.


Sagot :

To determine the relationship between the quantities in the given table, we can follow these steps:

[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & 13 \\ \hline 2 & 26 \\ \hline 3 & 39 \\ \hline 4 & 52 \\ \hline \end{tabular} \][/tex]

First, let's examine the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] by calculating the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair of values:

1. For [tex]\( x = 1 \)[/tex], [tex]\( y = 13 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{13}{1} = 13 \][/tex]

2. For [tex]\( x = 2 \)[/tex], [tex]\( y = 26 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{26}{2} = 13 \][/tex]

3. For [tex]\( x = 3 \)[/tex], [tex]\( y = 39 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{39}{3} = 13 \][/tex]

4. For [tex]\( x = 4 \)[/tex], [tex]\( y = 52 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{52}{4} = 13 \][/tex]

In each case, the ratio [tex]\( \frac{y}{x} \)[/tex] is consistently 13. This indicates that for every value of [tex]\( x \)[/tex], [tex]\( y \)[/tex] is 13 times [tex]\( x \)[/tex].

Hence, the relationship between the quantities [tex]\( x \)[/tex] and [tex]\( y \)[/tex] shown in the table is:

[tex]\[ y = 13x \][/tex]

So, the correct answer from the provided choices is:

The relationship between quantities is [tex]\( \times 13 \)[/tex].