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 accelerate if it were free to move on the slope under gravity. A skier is said to be "skiing the fall line" if he or she is moving generally down, making turns either side of the fall line, rather than moving across the slope.
Mathematically the fall line, the line of greatest slope, is the negative of the gradient (which points uphill) and perpendicular to the contour lines.