Slope field/Isocline

Slope fields are a way to visualize first order differential equations. They are most helpful in visualizing nonlinear ODEs. Consider an ODE $\dot x = f(x,t)$. A slope field is a plot of line segments with slope $f(x,t)$ in the $x,t$ plane.

In a slope field, an isocline is a curve along which each point has the same slope. In othe words, an isocline with value $C$ is the curve defined by the set of points $\{(x,t) : f(x,t) = C\}$.

The figure below shows a slope field with the $f(x,t) = 0$ isoclines shown as a dashed line. All line segments along the dashed lines have zero slope.

An isocline along which the slope is zero is called a nullcline.