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) \(k = -k\)

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?