Fibo Math Lab
Slope Field Lab
Skill goal: Read a slope field and sketch solution curves through initial points.
1 · Observe
Each short segment shows the slope dy/dx at that point — the direction a solution curve must travel there. Teal segments rise (positive slope), blue segments fall (negative slope), gray segments are flat (zero slope).
Window: x and y both run from −3 to 3.
2 · Manipulate
Tap anywhere on the field to drop an initial point (gold dot) — a solution curve is traced through it with tiny Euler steps (h = 0.05), forward and backward. Tap again for more curves; each gets its own teal shade.
Try it: on dy/dx = x, tap (0, 1). The traced curve hugs the analytic solution y = x²/2 + 1 and passes through (2, 3).
3 · Predict
4 · See
Move your pointer or finger over the field to read the slope at any point.
5 · Explain
Why it works: a slope field shows the direction a solution must follow at every point — without solving the equation first. The solution curve through an initial point threads through those directions like a path following signposts. That is why every curve you tap hugs the field, and why two solution curves never cross: at any single point there is only one signpost.