To identify which relation contains the ordered pair [tex]\((2, 7)\)[/tex], we need to substitute [tex]\(x = 2\)[/tex] into each given equation and see if the result equals [tex]\(y = 7\)[/tex].
First, let's use the equation [tex]\(y = 4x - 1\)[/tex]:
[tex]\[ y = 4(2) - 1 = 8 - 1 = 7 \][/tex]
This matches [tex]\(y = 7\)[/tex], so the first equation holds true for the ordered pair [tex]\((2, 7)\)[/tex].
Second, let's use the equation [tex]\(y = \frac{7}{x}\)[/tex]:
[tex]\[ y = \frac{7}{2} = 3.5 \][/tex]
This does not match [tex]\(y = 7\)[/tex], so the second equation does not hold true for [tex]\((2, 7)\)[/tex].
Next, let's use the equation [tex]\(y = \frac{2}{7} x\)[/tex]:
[tex]\[ y = \frac{2}{7} \cdot 2 = \frac{4}{7} \approx 0.57 \][/tex]
This does not match [tex]\(y = 7\)[/tex], so the third equation does not hold true for [tex]\((2, 7)\)[/tex].
Finally, let's use the equation [tex]\(y = \frac{7}{2} x\)[/tex]:
[tex]\[ y = \frac{7}{2} \cdot 2 = 7 \][/tex]
This matches [tex]\(y = 7\)[/tex], so the fourth equation holds true for the ordered pair [tex]\((2, 7)\)[/tex].
The only equation that contains the ordered pair [tex]\((2, 7)\)[/tex] and represents a direct variation is:
[tex]\[ y = 4x - 1 \][/tex]
Therefore, the correct relation is:
[tex]\[ y = 4x - 1 \][/tex]
