This is your choice but play lines can either be painted onto your playing surface, tufted in or inlaid. Tufted lines are incorporated into the carpet during production and are an integral part of the carpet. Inlaid lines are cut into the carpet during installation. (You really have to cut in circular and rounded sport lines.)
Both types of lines provide permanent markings that reduce on-going maintenance costs.
The down side is that carpets can and do move especially the carpets that are laid without a perimeter gripper system. (Just like the carpets you have at home)
When carpets move the lines start to waver and this is most obviously seen looking along the side lines.
The secondary downside to cut in lines is that these are areas of weakness and are most likely to be the first failure points when the carpets wear down. (However, where lines are cut in, the resulting join/seam in the carpet becomes a Painted lines can give greater flexibility to the use of the area and reduce the amount of seams that would be required for complex lining schemes. But they have to be reapplied annually at some cost.
The second point is that over time the paint can build up in the carpet which forms hard spots that during colder conditions can cause the balls bouncing or crossing these points to lift off the surface.
If you decide to go with a painted system then the choice is to use an acrylic paint or a two pack polyurethane system. Putting these paints down depends on weather conditions (Dry and warm) They do not work in wet conditions and must be given adequate time to set before being played on.