What is a slope field?

From Problem Set 1: Exercise 1.1

The slope field of a first order ODE, is a way to graphically display the solutions to the specified differential equations.

It is made of several line segments, each of which has a slope determined by the ODE. This means that the slopes of these line segments is the value of the derivative term from the ODE, or the -form term.

Each arrow or line segment is actually the tangent to the actual solutions at that point.

Slope fields can be helpful to understand the overall behavior of the ODE as the variables involved change value.