Slope Fields

At each point $(x, y)$, a short line segment shows the slope given by $\frac{dy}{dx}$.

1. Pick grid points.
2. Calculate $\frac{dy}{dx}$ at each.
3. Draw small segments with that slope.

• $\frac{dy}{dx} = x$: slopes depend only on $x$ (same slope in each column).
• $\frac{dy}{dx} = y$: slopes depend only on $y$ (same slope in each row).
• $\frac{dy}{dx} = x + y$: slopes depend on both.

Starting from an initial point, follow the slopes to trace a solution curve.