Answer
Vector form:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$;
Parametric form is: $x=1-t, y=3t$
Work Step by Step
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: $x=1-t, y=3t$
