# Tangent Line Formula

The line that touches the curve at a point called the point of tangency is a tangent line. Take a look at the graph to understand what is a tangent line. A curve that is on the line passing through the points coordinates (a, f(a)) and has slope that is equal to f’(a).

The **Tangent Line Formula** of the curve at any point ‘a’ is given as,

\[\large y-f(a)=m(x-a)\]

Where,

*f(a)* is the value of the curve function at a point ‘*a*‘

*m* is the value of the derivative of the curve function at a point ‘*a*‘

Solved Examples

**Question 1: **Find the tangent line of the curve f(x) = 4x^{2 }– 3 at x_{0} = 0 ?

**Solution:**

Given:

f(x) = 4x^{2} – 3

x_{0 }= 0

f(x_{0}) = f(0) = 4(0)^{2} – 3 = -3

f'(x) = 8x

m = f'(x_{0}) = 8(0) = 0

The tangent line formula is,

y – f(x_{0}) = m(x – x_{0})

y + 4 = 0(x – 0)

y + 4 = 0

The tangent of the curve is, y + 4 = 0