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Bunuel
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M07-29 [#permalink] New post  15 Sep 2014, 23:35
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Which of the following lines is parallel to line \(x = 4 - 2y\)?

A. \(y=2x+4\)
B. \(y=-2x-4\)
C. \(\frac{x}{2} - y = 4\)
D. \(y + \frac{x}{2} = 4\)
E. \(2y=2-\frac{1}{2}x\)
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Bunuel
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Re M07-29 [#permalink] New post  15 Sep 2014, 23:35
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Official Solution:

Which of the following lines is parallel to line \(x = 4 - 2y\)?

A. \(y=2x+4\)
B. \(y=-2x-4\)
C. \(\frac{x}{2} - y = 4\)
D. \(y + \frac{x}{2} = 4\)
E. \(2y=2-\frac{1}{2}x\)


Rewrite \(x = 4 - 2y\) as \(y=2-\frac{1}{2}x\), so the slope if this line is \(-\frac{1}{2}\). Now, since parallel lines have the same slope then a line parallel to the given line must also have the same slope.

Option D satisfies this. (\(y + \frac{x}{2} = 4\) is the same as \(y=4-\frac{1}{2}x\)).


Answer: D
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M07-29 [#permalink] New post  29 Nov 2019, 08:14
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Bunuel wrote:
Which of the following lines is parallel to line \(x = 4 - 2y\)?

A. \(y=2x+4\)
B. \(y=-2x-4\)
C. \(\frac{x}{2} - y = 4\)
D. \(y + \frac{x}{2} = 4\)
E. \(2y=2-\frac{1}{2}x\)



Two lines are parallel if they have the same slope.

Slope of given line :
\(x = 4 - 2y\)
\(4 - x = 2y\)
\(2+(-1/2)x=y\)
Comparing it with y=mx+c gives us m (slope) as -1/2

A quick scan through options will make you realise C or D are likely choices. Once you solve D is the right answer with slope as \((-1/2)\)
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Re: M07-29 [#permalink] New post  29 Nov 2019, 15:12
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Bunuel wrote:
Which of the following lines is parallel to line \(x = 4 - 2y\)?

A. \(y=2x+4\)
B. \(y=-2x-4\)
C. \(\frac{x}{2} - y = 4\)
D. \(y + \frac{x}{2} = 4\)
E. \(2y=2-\frac{1}{2}x\)


Caveat: I would just like to point out that it is not beyond the question-writers to place a trick answer among the responses that would correspond to the same line, rather than to one that was actually parallel. Yes, the slope of parallel lines must be the same, but the y-intercept must also be different, or else the two apparent lines would be one and the same. I could easily see an answer such as \( \frac{x}{2} = 2 - y\) appearing on the test, more likely in slots (A), (B), or (C) to snare some unwitting test-taker who might be in a hurry.

- Andrew
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hiranmay
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Re: M07-29 [#permalink] New post  20 Aug 2020, 08:04
Which of the following lines is parallel to line \(x = 4 - 2y\)? --> 2y =-x+4 => \(y= -\frac{1}{2}x+2\) --> slop of \(-\frac{1}{2}\)

A. \(y=2x+4\) --> not parallel: slop = +2
B. \(y=-2x-4\) --> not parallel: slop = -2
C. \(\frac{x}{2} - y = 4\) --> not parallel: slop = \(+\frac{1}{2}\)
D. \(y + \frac{x}{2} = 4\) --> correct: slop = \(-\frac{1}{2}\)
E. \(2y=2-\frac{1}{2}x\) --> not parallel: slop = \(-\frac{1}{4}\)

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