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

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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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Comments

JohnSep 2

thanks, this one was quick once I realized I just needed to test integer values for x.

AyushJun 21

wait why isn't it D? I plugged in x=3 and got an integer y...

RaymondJun 28

yeah 3 works for D. the question asks which one NEVER hits an integer point, so keep checking other x's

AmishaJun 23

B was my pick, the +1/3 is what throws off the whole line. any integer x still gives a non-integer y

GaisJul 4

exactly, that constant shift is the giveaway here

SuraiyaJul 20

easy but I second-guessed myself on E for a sec lol. the x/3 in both D and E had me testing a few values before deciding

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.