if x and y are defined as indicated by the accompanying table, which equation correctly represents the relationship between x and y?

x y
____
2 1
3 3
5 7
7 11

A. x+y=2
B.2x+y=2
C.2x+y=3
D.2x-y=3

1 answer

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:

  1. A. \( x + y = 2 \)

    • For \( x = 2, y = 1: 2 + 1 = 3 \) (not valid)
    • This does not fit.
  2. B. \( 2x + y = 2 \)

    • For \( x = 2, y = 1: 2(2) + 1 = 4 + 1 = 5 \) (not valid)
    • This does not fit.
  3. C. \( 2x + y = 3 \)

    • For \( x = 2, y = 1: 2(2) + 1 = 4 + 1 = 5 \) (not valid)
    • This does not fit.
  4. 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. \( 2x - y = 3 \).