How to prove that a function is a chord connecting two points

Question

I'm wondering of how to prove that the function $h (\lambda) = \lambda f (x_1)+(1-\lambda) f(x_2)$ is geometrically depicted as a chord connecting the points $(x_1, f (x_1))$ and $(x_2, f (x_2))$ in the Cartesian plane for any $x_1, x_2 \in X$ and any $\lambda\in [0, 1]$

if $f : X \to R$, with $X \subseteq R$. Any help is appreciated.

Answer 1

Write $h$ as $h(\lambda)=(f(x_1)−f(x_2))\lambda+f(x_2)$, which shows it is affine in $\lambda$, so it is a line ("chord"). Next, $h(0)=f(x_2)$ and $h(1)=f(x_1)$, so it connects the two points.