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 = bB)

k = 1C)

b + k = 0D)

|k| - 1 = 0E)

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-1k=1What do you think?