Good morning,
if you have 2 points then you can get 4 different equations which describe exactly the same straight line. Using your points A(3,1,-0) and B(4,0,2) with the stationary vectors $\displaystyle \vec a = \overrightarrow{OA}$ and $\displaystyle \vec b = \overrightarrow{OB}$ you'll get:
$\displaystyle l: \vec r = \vec a + \lambda(\vec b - \vec a)$
$\displaystyle l: \vec r = \vec a + \sigma( \vec a- \vec b )$
$\displaystyle l: \vec r = \vec b + \tau(\vec b - \vec a)$
$\displaystyle l: \vec r = \vec b + \rho( \vec a- \vec b )$