Hi, this is the title song from Gerry Raferty, called "Right Down the line". It means "all along" . It can also mean fully or thoroughly.

In what context? This means something traveled a path that was consistent with a line of some kind. However, "the line" could be lots of things. "The baseball player hit one right down the line." He hit a baseball, which traveled very close to one of the lines on the field. "The train moved right down the line." A train was traveling on train tracks. "The new computers moved right down the line in the factory." Some computers were produced using an assembly line.