I am not taking algebraic geometry or trying to prove anything. I'm just looking for a simple intuitive understanding of Bézout's theorem for the case when one of the curves is a constant function. From https://en.wikipedia.org/wiki/B%C3%A9zout%27s_theorem#Examples we have the example: "Two distinct non-parallel lines (in the same plane) always meet in exactly one point. Two parallel lines intersect at a unique point that lies at infinity."
But take y = 1 and y = x. These two lines meet once at (1,1), but the product of the degrees of these curves is 0*1 = 0.
I feel like I'm missing something very simple or don't understand the hypotheses of the theorem... can someone please help explain? Thanks!