Given an ordinary differential equation 
, the slope field for that differential
equation is the vector field that takes a point 
to a unit
vector with slope 
. The vectors in a slope field are usually drawn without
arrowheads, indicating that they can be followed in either direction. Using a visualization
of a slope field, it is easy to graphically trace out solution curves to initial
value problems. For example, the illustration above shows the slope field for
the equation 
together with solution curves for various initial values of 
.
