$(\Delta_1): y = k_1x + m_1$
$\to (\Delta_1): k_1x - y + m_1 =0$
$\to \overrightarrow{n_1} = (k_1;-1)$ là $\rm VTPT$ của $(\Delta_1)$
$(\Delta_2): y = k_2x + m_2$
$\to (\Delta_2): k_2x - y + m_2 =0$
$\to \overrightarrow{n_2} = (k_2;-1)$ là $\rm VTPT$ của $(\Delta_2)$
Ta có:
$(\Delta_1)\perp (\Delta_2) \Leftrightarrow \overrightarrow{n_1} \perp \overrightarrow{n_2}$
$\Leftrightarrow k_1k_2 + (-1).(-1) =0$
$\Leftrightarrow k_1k_2 + 1 =0$
$\Leftrightarrow k_1k_2 = -1$
Vậy $$\boxed{(\Delta_1)\perp (\Delta_2) \Leftrightarrow k_1.k_2 = -1}$$
