sanaa.rizwan wrote:QR PS 83
Which of the following lines in the xy plane does not contain any points with integers as both coordinates
A. Y = x
B. Y = x + 1/2
C. Y = x + 5
D. Y = ½ x
E. Y = ½ x + 5
If x and y are both integers, then their DIFFERENCE must also be an integer.
Answer choice B, rephrased: y-x = 1/2.
Since the difference between x and y here is not an integer, x and y cannot both be integers.
The correct answer is
B.
An alternate approach is to show that x and y CAN both be integers in four of the five answer choices.
Plug x =2 into the answer choices:
A: y = x = 2. Since x and y are both integers, eliminate A.
B: y = x + 1/2 = 2 + 1/2 = 2.5. Since y is not an integer, hold onto B.
C: y = x + 5 = 2+5 = 7. Since x and y are both integers, eliminate C.
D: y = (1/2)x = (1/2)2 = 1. Since x and y are both integers, eliminate D.
E: y = (1/2)x + 5 = (1/2)2 + 5 = 6. Since x and y are both integers, eliminate E.
The correct answer is
B.
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