line segment

Line segment

$$\begin{array}{rl}y& =\theta x_1+(1-\theta )x_2\\ & =x_2+\theta (x_1-x_2)\end{array}$$

$x_1\ne x_2$ are two points $\in {\mathbb{R}}^n$
$\theta \in \mathbb{R}$ form the line passing through $x_1$ and $x_2$
$\theta =1\to y=x_1$
$\theta =0\to y=x_2$
Values between 0 and 1 give points on the (closed) line segment between $x_1$ and $x_2$

$x_1-x_2$ is the direction which points from $x_2$ to $x_1$. As $\theta$ increases from $0$ to $1$, the point $y$ moves from $x_2$ to $x_1$.