Answer:
Folk and Country Music are one in the same. Country Music as an art form was derived from the old folk songs sung by Mountain folk, Farmers, Sharecroppers, and can even be traced to days of Slavery.
A.P. Carter, the head of the Legendary "Carter Family" who some credit as the founders of Country Music, travelled around the Country "a lot in the rural south" bringing songs back from Appalachian musicians, "Hill Folk". He made it his mission to bring these songs to the masses, because in those days the songs would have otherwise been lost. The poor Mountain musicians didn't have telephones, and without cars they traveled no further than their own small communities.
During this time, "Hillbilly Music" as it was referred to then began to gain popularity. It wasn't until the 1940's that we began to call it Country Music as the term hillbilly had become degrading and stereotyped. As the music continued to gain some mainstream popularity we spawned legendary artists such as Gene Autry, Roy Acuff, Ernest Tubb, Hank Williams Sr, and then later Superstars like George Jones, Merle Haggard, Johnny Cash, Waylon Jennings and so on.
So without folk music there would not be a Country Music today. I hope this answers your question!