Why has a crack appeared down my wall?
get a ref to a pro building inspector to determine the reason for this maybe from home depot,where the guys leave business cards a local real estater can help building stresses may come from a number of sources local geological shifting which no one can do anything about a bad pour of masonry for the basement floor,a source of water leaking, excess loads on the floor ceiling members, a tembler that shook the house causing walls to crunch & grind then pop out, or yer nephew playing dottgam rock & roll too loud,kiddies jumping up stairs in a big party I useda love doing that,,back int he day
You not only have a crack, you have some water damage bubbling the wallboard and paint. I would guess that you have a small roof leak that is following a pipe and studs until it travels along that wallboard seam, making it warp and bubble. You should check the area over your kitchen to see if the flashing around vent pipes or attic vents might need to be resealed to prevent water backup and leakage.
No one here can tell you WHY it's appeared, because we're not seeing it and we know nothing about the conditions. As for dealing with it, I would strongly suggest you consult with a licensed carpenter or carpentry contractor.
Assuming you don't have earthquakes and haven't had any roller hockey going on in your house recently, then it's likely from the ground settling under your house. This can happen even on older homes depending on the type of soil you have, the amount of rain you have or haven't had the last few years, and other such factors. If it continues to expand then you may want to get it looked at but otherwise it's nothing some sparkle and paint won't cover.
the usual cause is shifting foundation. Other possible causes, not very likely, include improper original construction, incorrect construction during remodeling, and the wall being struck by falling objects such as trees during high wind events. What you do is inspect the foundation as best you can to see if the earth has been subsiding. As long as the crack stops growing, most folk ignore them [or fill the crack with joint compound and repaint over it]. In a few areas of the country, you have to inspect closely for a possible sinkhole under the house. This is a professional job -- echo sounding equipment is used to judge the density of the underlying earth.
That is a settlement crack. Very common and nothing to worry about. Cracks that are of concern are diagonal stepped cracks often near a window or door.