# Linear transformation from [-1,1] to [a,b]

Hey
This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from [-1,1] to [a,b] as: x = 2/(b-a) * z - (b+a)/(b-a)
what is the proof of this tranformation? where did it come from?
thanks

$$-1 = ma + c \\ 1 = mb + c$$