# Slope Fields

## Slope Fields

Slope fields can be used to visualize the solutions of a first order differential equation of the form \[ \frac{dy}{dx} = f(x,y) \] where \(y\) is a function of \(x\). At any point \((x,y)\) in the Cartesian plane, the value of \(\frac{dy}{dx} = f(x,y)\) gives us the slope of the tangent line to the graph of the differential equation's solution. By drawing short line segments with that slope at several points, we can begin to see the "shape" of the solutions of the differential equation.## About the Applet

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