The process of obtaining the derivative of a function is called . Refer to the diagram given. Gradient, m = tan α. In terms of P, Q and R, what is tan α equal to? Find the gradient of the line passing through the points (1, 2) and (4, 8).

The process of obtaining the derivative of a function is called differentiation.
Answer for 1: $\boxed{\text{Differentiation}}$

From the diagram, the 'rise' corresponds to the length of the segment QR, and the 'run' corresponds to the length of the segment PR.
The gradient $m = \tan \alpha = \frac{\text{rise}}{\text{run}}$.
Therefore, in terms of P, Q, and R:

Answer for 2: $\boxed{\frac{QR}{PR}}$

The given points are $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (4, 8)$.
The formula for the gradient $m$ of a line passing through two points is:

Substitute the given coordinates into the formula:

Answer for 3: $\boxed{2}$