Interactive resource
Interactive Slope (Direction) Fields
Calculus. See dy/dx = f(x,y) as tiny slopes on a grid — intuition for differential-equation solution curves. Free interactive GeoGebra resource — adjust…
Overview
A slope field draws the instantaneous direction at each point. Solution curves stay tangent to those segments.
Explanation
A slope field draws the tangent direction given by dy/dx = f(x,y) at each point.
Solution curves stay tangent to these segments.
Changing the equation reveals spreading, clustering, or equilibria.
How to use
- Open the slope-field scene.
- Switch equation types.
- Adjust parameter k.
- Imagine curves threading along the short segments.
What to watch
Choose dy/dx = ky and notice how segments flatten near the equilibrium y = 0.
Knowledge points
FAQ
Do students need to solve DEs first?
Use this for geometric intuition; solving can come later.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.