The equation of one of the straight lines which passes through the...

$y = mx + c$

$3 = m + c$

$\sqrt{2} = \left|\dfrac{m - 3\sqrt{2}}{1 + 3\sqrt{2}m}\right|$

$⇒ 6m + \sqrt{2} = \pm \left(m - 3\sqrt{2}\right)$

from Positive sign

$⇒ 5m = - 4\sqrt{2} ⇒ m = \dfrac{- 4\sqrt{2}}{5}$

from negative sign

$⇒ 6m + \sqrt{2} = - m + 3\sqrt{2}$

$⇒ 7m = 2\sqrt{2} ⇒ m = \dfrac{2\sqrt{2}}{7}$

According to options take $m = \dfrac{- 4\sqrt{2}}{5}$

So $y = \dfrac{- 4\sqrt{2}x}{5} + \dfrac{3 + 4\sqrt{2}}{5}$

$4\sqrt{2}x + 5y - ( 15 + 4\sqrt{2} ) = 0$