# Math Insight

### Applet: Line parametrization

The blue point $\color{blue}{\vc{x}}$ sweeps out the line parameterized by $\color{blue}{\vc{x}} = \color{red}{\vc{a}} + t\color{green}{\vc{v}}$, where $\color{red}{\vc{a}}$ is the red point and $\color{green}{\vc{v}}$ is the green vector. Change the line by dragging the red point or green arrow heads. Change the position of $\color{blue}{\vc{x}}$ along the line by dragging either the point itself or the cyan dot on the slider that determines the value of $t$. Dragging elsewhere on the figure rotates the graph.

Notice that when $t=0$, then $\color{blue}{\vc{x}}=\color{red}{\vc{a}}$. And when $t=1$, $\color{blue}{\vc{x}}$ is on top of the endpoint of the vector $\color{green}{\vc{v}}$, which is at position $\color{red}{\vc{a}}+\color{green}{\vc{v}}$.