# Tangent Line

Tangent line is a line that just touches a curve at one point without cutting across it. It can be a line through a pair of infinitely close points on the curve. Formally it is a line which intersects a differentiable curve at a point where the slope of the curve is equal to the slope of the line.

The word tangent comes from the latin word tangere means to touch. First definition of tangent line was 'a right line which touches a curve, but which when produced, does not cut it'. Tangent line just touches the surface of the curve at a point and the point at which it touches the curve is called the point of tangency.