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

Question

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

Answer 1

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. $2x-y=3$.