The slope of the line, 3x – $2\sqrt2y$ – 4 = 0 is:

1. $\dfrac{3\sqrt{2}}{2}$

2. $\dfrac{-3\sqrt{2}}{2}$

3. $\dfrac{3\sqrt{2}}{4}$

4. $-\dfrac{3\sqrt{2}}{4}$

Solving,

$\Rightarrow 3x - 2\sqrt{2}y - 4 = 0 \\[1em] \Rightarrow -2\sqrt{2}y = -3x + 4 \\[1em] \Rightarrow y = \dfrac{-3}{-2\sqrt{2}}x + \dfrac{4}{-2\sqrt{2}} \\[1em] \Rightarrow y = \dfrac{3}{2\sqrt{2}}x - \dfrac{2}{\sqrt{2}}.$

Comparing above equation with y = mx + c, we get :

m = $\dfrac{3}{2\sqrt2}$

Rationalizing the Denominator,

$m = \dfrac{3}{2\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} \\[1em] = \dfrac{3\sqrt{2}}{2 \times 2} \\[1em] = \dfrac{3\sqrt{2}}{4}.$

Hence, option 3 is the correct option.