# Slope Fields

- Author:
- Ken Schwartz

- Topic:
- Differential Equation

A slope field is a collection of short line segments, whose slopes match that of a solution of a first-order differential equation passing through the segment's midpoint. The pattern produced by the slope field aids in visualizing the shape of the curve of the solution. This is especially useful when the solution to a differential equation is difficult to obtain analytically.

Enter the differential equation in the "dy/dx" input box. You can set the look of the slope field using the three sliders. "Field Size" sets the size of the slope field, which is always a square centered on the origin. "Density" sets the number of line segments across the field. "Length" sets the length of the segments. The "Show Slope Field" box can be unchecked so you can work out slope field problems before checking the answer.
You can view or hide the particular solution that passes through an initial condition by checking or clearing the "Show Solution" box. To set the initial condition, drag the large red dot to the coordinates of the initial condition.