Why must a line pass the origin if the product of x and y intercept is zero?

Related to Question 13. Because, if we have a perfectly horizontal line, i.e. y=2, the y intercept is 2, but there is no x-intercept, so the product will also be zero, without the line ever crossing the origin.

How? “no x-intercept” is not synonymous with having an x-intercept of 0,

I see