Show that the parametric equation $ x=x_1+(x_2-x_1)t , y=y_1+(y_2-y_1)t$ Can anyone help me to solve this?
Show that the parametric equation
$ x=x_1+(x_2-x_1)t $
$ y=y_1+(y_2-y_1)t\ $
with $(0\le t\le 1)$
describe the segment that joint the point $P_1=(x_1,y_1)$ and 
$P_2=(x_2,y_2)$
Thanks all

Let us use the idea of vector. Any point $(x,y)$ on the segment can be represented as
$$x=x_1+(x_2-x_1)t, y=y_1+(y_2-y_1)t$$
where $0\le t\le 1$
because $(x_1,y_1)$ is the start point and $(x_2-x_1, y_2-y_1)$ is the orientation vector from $(x_1,y_1)$ to $(x_2,y_2)$.
Let $O(0,0), A(x_1,y_1),B(x_2,y_2), P(x,y)$ where $P$ represents any point on the segment.
$$\vec{OP}=\vec{OA}+t\vec{AB}=\vec{OA}+t(\vec{OB}-\vec{OA})$$
where $0\le t\le 1$. You'll see that this is the same representation as above.
