tangent line

A straight line that touches a curve at a single point and matches the curve's direction there. Its slope at the point of contact equals the derivative of the function at that point: `m_tangent = f'(a)`. The tangent is what the secant becomes in the limit as its two intersection points merge — the curve's _instantaneous direction_ made visible as a line. Distinct from the trigonometric tangent; same word, different concept.