Identify which of the following lines in the xy-plane does not intersect at any point where both coordinates are integers.

Answer Choices

Correct answer marked below

y=x+3

y=x+\frac{1}{3}

Correct

y=x+7

y=\frac{1}{3}*x

y=\frac{1}{3}*x +7

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Explanation

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Official Explanation

Official

We need to determine which line does not have integer solutions for both coordinates. The lines are:

(A) y = x + 3,

(B) y = x + 1/3,

(C) y = x + 7,

(D) y = x * 1/3, and

(E) y = x/3 + 7.…

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What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.