It looks like
I think you would need to know the point where the two equations intersect to determine what the actual value of k is.
If I had to guess at an answer, I'd say it's because they don't cross each other, if they could cross each other they could clearly touch the same point with different tangent lines. But, thats just a guess.
Also, how would you solve for x at this point? I can see that the point would be But I don't know how to solve for it without just being able to "see" the answer.