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Math Expert V
Joined: 02 Sep 2009
Posts: 59588

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Difficulty:   15% (low)

Question Stats: 74% (00:54) correct 26% (01:01) wrong based on 107 sessions

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 59588

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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 $$y=4-\frac{1}{2}x$$).

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Director  P
Joined: 18 Dec 2017
Posts: 826
Location: United States (KS)

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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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Manager  G
Joined: 16 May 2019
Posts: 138

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1
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 Re: M07-29   [#permalink] 29 Nov 2019, 16:12
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# M07-29

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