Here are two possible solutions:

SOLUTION A: Number sense
If x is an integer, then x + 1/2 is NOT an integer.
So, if y = x + 1/2, then it's impossible for x and y to both be integers
Answer: D


SOLUTION B: Process of elimination (POE)
(A) \(y = 4\)
The integer coordinates x = 1 and y = 4 satisfy this equation.
Eliminate answer choice A

(B) \(y = \frac{1}{2}x\)
The integer coordinates x = 2 and y = 1 satisfy this equation.
Eliminate answer choice B

(C) \(y = x + 3\)
The integer coordinates x = 1 and y = 4 satisfy this equation.
Eliminate answer choice C

(E) \(y=\frac{1}{2}x+3\)
The integer coordinates x = 2 and y = 4 satisfy this equation.
Eliminate answer choice E

By the POE, the correct answer is D

Cheers,
Brent

The calculator gives wrong # when making sqr40 two consecutive times, it gives 2.445 while the answer is 2.51