Use google?

What kind of intersection you want to check for?

Some specific like line-plane (line-triangle?)?

Or do you want to know how to properly check for intersection with a big model with many triangles?

Or perhaps you want something like raycasting?

Here is how I would do it:

the distance from one point to another is sqrt( (X2 - X1)^2 + (Y2 - Y1)^2 + (Z2 - Z1)^2 )

The equation for your line is 0xi + 1yj + 0zk => yj

So you would want to see if that line ever comes closer to the center of the sphere than the radius of the sphere. So basically, is there any value of y (for your line) that would make the distance calculation above be less than or equal to R.