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M23 Q14

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M23 Q14 [#permalink] New post 23 Feb 2010, 12:57
I want to discuss following question:

If line y = kx + b is parallel to line x = b + ky , which of the following must be true?

A) k = b
B) k = 1
C) b + k = 0
D) |k| - 1 = 0
E) k = -k


[Reveal] Spoiler: OA:
D


[Reveal] Spoiler: OE:
For lines to be parallel, their slopes must be equal. The second equation can be rewritten as y = \frac{1}{k}*x - \frac{b}{k} . Because slopes must be equal, k = \frac{1}{k} or k^2 = 1 or |k| = 1 .



Obviously the slopes of the lines should be the same. But what about y-intercepts? If the slopes of two lines are same AND y-intercepts are also the same we in fact have the same line, not two parallel lines.

From equality of slopes we establish, that |k|=1, but I also thought that maybe -
b\neq-\frac{b}{k}
k\neq-1
k=1

What do you think?
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Re: M23 Q14 [#permalink] New post 13 Mar 2010, 11:58
shalva wrote:
I want to discuss following question:

If line y = kx + b is parallel to line x = b + ky , which of the following must be true?

A) k = b
B) k = 1
C) b + k = 0
D) |k| - 1 = 0
E) k = -k


[Reveal] Spoiler: OA:
D


[Reveal] Spoiler: OE:
For lines to be parallel, their slopes must be equal. The second equation can be rewritten as y = \frac{1}{k}*x - \frac{b}{k} . Because slopes must be equal, k = \frac{1}{k} or k^2 = 1 or |k| = 1 .



Obviously the slopes of the lines should be the same. But what about y-intercepts? If the slopes of two lines are same AND y-intercepts are also the same we in fact have the same line, not two parallel lines.

From equality of slopes we establish, that |k|=1, but I also thought that maybe -
b\neq-\frac{b}{k}
k\neq-1
k=1

What do you think?


It should be D, cos y intercept can be equal as it is given that lines are parallel but it is not given that lines are not equal.
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Re: M23 Q14   [#permalink] 13 Mar 2010, 11:58
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