At this point, you've replaced your line through P with a collinear segment through P . Change the length of Delta and observe the effect on the segment through P . Drag P about the sketch to confirm that the segment changes slope just as your line did. The segment at P shows you the slope at a single point. Dragging P shows the slope at every point of the drag.
Traced segments leaves image behind as they're dragged.
Using tracing here allows you to see the segment's shape at various positions of P simultaneously. Using snapping here allows you to drag P to uniformly-spaced positions in the plane. As you drag, the traced segment shows the slope local to each point on the lattice grid. Try to drag P so that you fill in the entire lattice. Then resume dragging until you've filled in segments for the entire slope field.