Variation Curves Lab
Drag k and watch direct variation steepen while inverse variation stretches — the same constant, two opposite behaviors, one canvas.
1 Variation Curves Lab
One slider for k, two curves: the blue line is y = kx (direct), the teal hyperbola is y = k/x (inverse).
k = 4
2 What to notice
Three experiments.
1. Same k, opposite behavior
At k = 4, the line climbs while the hyperbola falls. Bigger k steepens the line and pushes the hyperbola outward.
2. Negative k mirrors everything
Drag k below 0: the line falls and the hyperbola jumps to quadrants II and IV.
3. The hyperbola never touches the axes
y = k/x is undefined at x = 0 — the curve approaches but never reaches either axis.