WHY IS THE SLOPE OF A LINE TAN(THETA)?

We know that,

Slope of the line =  ....... (1)

Let θ be the angle.

Then in the right angled triangle, Perpendicular = y₂–y₁ and base =x₂–x₁

Therefore, tan θ =  ...... (2)

From (1) and (2), we get 

Slope of the line = tan θ