$\overrightarrow{n_{\Delta'}} = \left ( 1; -3 \right )$
$\to \overrightarrow{u_{\Delta'}} = \left ( 3; 1 \right )$
$\to \overrightarrow{n_{\Delta}} = \left ( 3; 1 \right )$
$\to PT \Delta : 3\left ( x - 1 \right ) + 1.\left ( y + \dfrac{3}{4} \right ) = 0$
$\to 3x - 3 + y + \dfrac{3}{4} = 0$
$\to 3x + y - \dfrac{9}{4} = 0$
$\to 12x + 4y - 9 = 0$