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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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