## Linear Algebra: A Modern Introduction

Vector form:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$; Parametric form is: $x=1-t, y=3t$
The vector form of a line is: $x=p+td$ This implies:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$ And: Parametric equations of a line are defined as the equations which are correspond to the components of the vector. Thus, the parametric form of the equation of the line is: $x=1-t, y=3t$ Hence, the vector form is:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$; Parametric form: $x=1-t, y=3t$