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23 Feb 2010, 12:57
Kudos
Bookmarks
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) \(k = -k\)
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?
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) \(k = -k\)
Show SpoilerOA:
D
Show SpoilerOE:
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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13 Mar 2010, 11:58
Kudos
Bookmarks
shalva
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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Thank you for understanding, and happy exploring!
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