To find the equation that correctly represents the relationship between \( x \) and \( y \), we can analyze the values in the table and see if we can identify a linear relationship.
We will test each potential equation to see if it holds true for all the pairs of \( (x, y) \):
Choices:
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A. \( x + y = 2 \)
- For \( x = 2, y = 1: 2 + 1 = 3 \) (not valid)
- This does not fit.
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B. \( 2x + y = 2 \)
- For \( x = 2, y = 1: 2(2) + 1 = 4 + 1 = 5 \) (not valid)
- This does not fit.
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C. \( 2x + y = 3 \)
- For \( x = 2, y = 1: 2(2) + 1 = 4 + 1 = 5 \) (not valid)
- This does not fit.
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D. \( 2x - y = 3 \)
- For \( x = 2, y = 1: 2(2) - 1 = 4 - 1 = 3 \) (valid)
- For \( x = 3, y = 3: 2(3) - 3 = 6 - 3 = 3 \) (valid)
- For \( x = 5, y = 7: 2(5) - 7 = 10 - 7 = 3 \) (valid)
- For \( x = 7, y = 11: 2(7) - 11 = 14 - 11 = 3 \) (valid)
- This fits for all pairs.
Thus, the correct equation that represents the relationship between \( x \) and \( y \) is
D. \( 2x - y = 3 \).