What is a slope of a line?

Question

What is a slope of a line? I understand that it is obtained by tan$\theta$ where $\theta$ is the inclination of the line but overall what does it means?

Answer 1

We can define slope of a line as following $$\text{slope of a straight line}\triangleq\\\text{The amount of vertical increment for any unit amount of horizontal increment}\\={\text{The amount of vertical increment}\over \text{The amount of horizontal increment}}$$which exactly suits the concept of tangent of an angle. Moreover, you can define the slope of tangent on a function is a specific point (provided there exists such a tangent at all for which we call the function differentiable at $x_0$) as $$\text{Slope of tangent on a function is point }x_0\triangleq\\{\text{Infinitely small vertical increment around }x_0\over \text{Infinitely small horizontal increment around }x_0}$$