In alpine skiing, a fall line refers to the line down a mountain or hill which is most directly downhill. That is, the direction a ball would roll if it were free to move on the slope under gravity. A skier is said to be "skiing the fall line" if he is skiing a line with his skis pointing generally down, rather than traversing across it.
Mathematically the fall line, the line of greatest slope, is the negative of the gradient (which points uphill) and perpendicular to the contour lines.