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Which of the following is an equation of a line that does NOT contain

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Which of the following is an equation of a line that does NOT contain  [#permalink]

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03 Dec 2019, 02:11
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Which of the following is an equation of a line that does NOT contain any points in the xy-plane for which both coordinates are integers?

A. $$y = 4$$

B. $$y=\frac{1}{2} x$$

C. $$y=x+3$$

D. $$y=x+\frac{1}{2}$$

E. $$y=\frac{1}{2}x+3$$

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Which of the following is an equation of a line that does NOT contain  [#permalink]

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04 Dec 2019, 14:43
y=4 is a horizontal line, meaning the y coordinate is always 4, and it takes on all x values, so we can eliminate A. B is a line with a slope of +1/2 that runs through the origin, meaning it will take the value (0,0), so B can be eliminated. C is a line with a slope of +1 and a y-intercept at 3, meaning it takes on the value of (0,3), so C can be eliminated. D is a line with a slope of 1 with a y intercept at 1/2. Since each x value that is an integer will have a y coordinate that has a .5 at the end, this line will not have an x and y coordinates that are integers, so D is the correct answer.
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Re: Which of the following is an equation of a line that does NOT contain  [#permalink]

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08 Dec 2019, 20:22
Bunuel wrote:
Which of the following is an equation of a line that does NOT contain any points in the xy-plane for which both coordinates are integers?

A. $$y = 4$$

B. $$y=\frac{1}{2} x$$

C. $$y=x+3$$

D. $$y=x+\frac{1}{2}$$

E. $$y=\frac{1}{2}x+3$$

If x is an integer, then x + ½ can never be an integer. Thus, in choice D, x and y can’t both be integers.

As an exercise, let’s show that all other lines contain points where both coordinates are integers: The points (0, 4), (2, 1), (0, 3) and (2, 4) are on the lines whose equations are given in answer choices A, B, C, and E, respectively.
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Re: Which of the following is an equation of a line that does NOT contain   [#permalink] 08 Dec 2019, 20:22
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