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Sagot :
To determine which table could represent the function [tex]\( y = 2x \)[/tex], where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex] and the constant of variation is 2, we need to verify the relationship [tex]\( y = 2x \)[/tex] for the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in each table.
Let's go through each table one by one and check if the values of [tex]\( y \)[/tex] correspond correctly to [tex]\( y = 2x \)[/tex]:
1. For the first table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 1 \\ \hline 4 & 2 \\ \hline 6 & 4 \\ \hline 8 & 8 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], but [tex]\( y = 1 \)[/tex].
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 2 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 4 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 8 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
2. For the second table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 4 \\ \hline 4 & 6 \\ \hline 6 & 8 \\ \hline 8 & 10 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], and [tex]\( y = 4 \)[/tex], this is correct.
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 6 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 8 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 10 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
3. For the third table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 8 \\ \hline 4 & 12 \\ \hline 6 & 16 \\ \hline 8 & 20 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], but [tex]\( y = 8 \)[/tex].
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 12 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 16 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 20 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
4. For the fourth table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 4 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], and [tex]\( y = 4 \)[/tex], this is correct.
This table represents the function [tex]\( y = 2x \)[/tex].
Therefore, the fourth table is the one that could represent the function [tex]\( y = 2x \)[/tex].
Let's go through each table one by one and check if the values of [tex]\( y \)[/tex] correspond correctly to [tex]\( y = 2x \)[/tex]:
1. For the first table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 1 \\ \hline 4 & 2 \\ \hline 6 & 4 \\ \hline 8 & 8 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], but [tex]\( y = 1 \)[/tex].
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 2 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 4 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 8 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
2. For the second table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 4 \\ \hline 4 & 6 \\ \hline 6 & 8 \\ \hline 8 & 10 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], and [tex]\( y = 4 \)[/tex], this is correct.
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 6 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 8 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 10 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
3. For the third table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 8 \\ \hline 4 & 12 \\ \hline 6 & 16 \\ \hline 8 & 20 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], but [tex]\( y = 8 \)[/tex].
- For [tex]\( x = 4 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 4 = 8 \)[/tex], but [tex]\( y = 12 \)[/tex].
- For [tex]\( x = 6 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 6 = 12 \)[/tex], but [tex]\( y = 16 \)[/tex].
- For [tex]\( x = 8 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 8 = 16 \)[/tex], but [tex]\( y = 20 \)[/tex].
This table does not represent the function [tex]\( y = 2x \)[/tex].
4. For the fourth table:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 4 \\ \hline \end{tabular} \][/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] should be [tex]\( 2 \times 2 = 4 \)[/tex], and [tex]\( y = 4 \)[/tex], this is correct.
This table represents the function [tex]\( y = 2x \)[/tex].
Therefore, the fourth table is the one that could represent the function [tex]\( y = 2x \)[/tex].
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