Parametrics, when $t$ is not in between $0<t<1$

Question

I understand how to parameterize a line segment when the $t$ value lies in between $0$ and $1$, however I was wondering how to create a parametric equation for the line segment between say $(1.5,2)$ and $(3,0)$ but now t must lie between $1$ and $2$. Any help would be greatly appreciated.

Answer 1

Geometrically, we have a straight line if we have a point along with a direction. The line segment joining $(1.5,2)$ and $(3,0)$ is the set $$\{ (1.5, 2) + t[(3,0) - (1.5,2)] \mid t \in [0,1] \} = \{ (1.5,2) + t(1.5,-2) \mid t \in [0,1] \};$$ in fact, for all $a,b \in \mathbb{R}^{n}$ the line segment joining $a$ and $b$ is the set $L := \{ a + t(b-a) \mid t \in [0,1] \}$. To parametrize $L$ it suffices to use the map $t \mapsto a+ t(b-a): [0,1] \to \mathbb{R}^{n}$.