A first-order DE dy/dx = f(x, y) assigns a slope to each point (x, y) in the plane, creating a slope field (direction field). Solution curves are tangent to these slopes everywhere. This geometric view helps in understanding: (1) Why initial conditions give unique solutions — you follow the slopes from a starting point. (2) Why singular solutions (envelopes) exist — they are tangent to all member curves. (3) Isoclines — curves along which the slope is constant (f(x,y) = c) — help in sketching solutions. In JEE, this interpretation is used in problems like "the curve passing through (1,1) whose tangent at any point (x,y) has slope 2y/x" — just set dy/dx = 2y/x and solve with y(1) = 1.