$$y=f'(x_0)\cdot (x-x_0)+f(x_0)$$

$$y=0$$

In mathematics, a tangent line is a straight line that touches a curve or a function at a single point without crossing it. At the point of contact, the tangent line has the same slope as the curve, representing the instantaneous rate of change of the function at that specific location. Tangent lines are used to approximate the behavior of a function near a particular point and are fundamental in calculus for understanding local properties of functions and finding critical points.