# Tangents and Normals: Derivative As Measure Of Slope

Consider a curve whose equation is y = f(x). On this curve, take a point P(x_{1},y_{1}).

Assuming that the tangent at this point is not parallel to the coordinate axes, the equation of the tangent line at P is the equation of a straight line with slope gradient m passing through (x_{1},y_{1}).

y – y_{1} = m(x – x_{1})

The slope **m = f′(x _{1}) = dy/dx** at (x

_{1},y

_{1})

The equation of the tangent is of the form

y – y_{1} = f′(x_{1})(x – x_{1})

### Normal

The normal to a curve at a given point is a straight line passing through the given point, perpendicular to the tangent at this point.

The slope of the normal m′ and that of the tangent m are connected by the equation

m′ = – 1/m

The equation of a normal to a curve y = f(x) at a point P(x_{1},y_{1}) is

**y – y _{1} = m′(x – x_{1})**