From Bishop's book pag 183 - (4.11) (Pattern Recognition and Machine Learning, 2009), a mathematical relationship is immediately shown without an explanation of where it is derived from:
I cannot understand where 4.11 comes from and the meaning of the lambda parameter prensent in the formula
Suppose you have two vectors (points in $\mathbb{R}^n$) called $x$ and $y$. Now, any point on the line between $x$ and $y$ is of the form $x + t(y-x).$ This is because the formula I just wrote is saying that "you start from $x$, then move $t$ units along the vector $y-x$," where $y-x$ is the line passing through $y$ and $x$. Then notice that $$x + t(y-x) = x(1-t) + yt,$$ which is the expression in the above.