Mathematics

A horizontal line segment means the slope is zero at that point, so $\frac{dy}{dx} = 0$ there. This tells you that a solution curve passing through $(x_0, y_0)$ has a flat tangent line—it's neither rising nor falling at that instant. Recognizing where $\frac{dy}{dx} = 0$ helps you spot equilibrium solutions and turning points where the behavior of solutions changes.

A horizontal line segment means the slope is zero at that point, so $\frac{dy}{dx} = 0$ there. This tells you that a solution curve passing through $(x_0, y_0)$ has a flat tangent line—it's neither rising nor falling at that instant. Recognizing where $\frac{dy}{dx} = 0$ helps you spot equilibrium solutions and turning points where the behavior of solutions changes.