[Math] Derivation of linear interpolation

Question

Anyone know a good derivation of the linear interpolation:

$$\frac{y-y_0}{x-x_0}=\frac{y_1-y_0}{x_1-x_0}$$

Wikipedia gives one, which I don't understand.

Answer 1

Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.