# What is a slope field of a differential equation?

This is basically a graphical representation of many derivatives of one function, including vertical shifts, illustrating how the solution to an indefinite integral involves all vertical shifts, "$+ C$"
A slope field is a way of describing the function $f \left(x\right) + C$ by tracing its derivative at multiple points within a viewing window, including all of its vertical shifts.
When you see a slope field like this, if you simply connect the dashes together and make a curve, you trace the curve itself at some $+ C$ shift. Each dash corresponds to a single derivative at some value of $x$.