I don't agree that all lines have a y-intercept. After all, it is possible to have a line that is vertical and parallel to the y-axis. In such a case, the line would not cross the axis and would have no intercept.

Granted, this line cannot be described in a y = mx + b equation. It has to be defined simply as (for example) x = 2. But still, such a line can exist and it would be graphed as a vertical line that intersects the x axis at (2,0).

Not all the lines have x intercepts.

For instance, a constant function f(x)=c is represented by a line that is parallel to x axis, never intercepting it.

Instead, all lines have y intercepts.

We'll have an example

y = mx+n

m is the slope of the line and n is y intercept

We'll calculate x intercept:

y = 0 <=> mx+n = 0 <=> x = -m/n

The intercepting point is (-m/n , 0)

We'll calculate y intercept:

x = 0 <=> y=m*0+n <=> y=n

The intercepting point is (0 , n).