Consecutive points are connected by line segments. A new line is only needed when the slope of segment (i, i+1) differs from the slope of segment (i+1, i+2). Start with count = 1 for at least 2 points.

Compare slopes using cross-multiplication: (y2−y1)·(x3−x2) !== (y3−y2)·(x2−x1). This avoids floating-point division and works for vertical/horizontal segments.

Points are already sorted by x (day), but ensure no two consecutive points share the same x — if they do, the segment is vertical and the slope formula with cross-multiplication still handles it. A single point returns 0 lines.