Find the slope of the line which is perpendicular to $\dfrac{x}{3} - 2y = 4$.

Given,

$\Rightarrow \dfrac{x}{3} - 2y = 4 \\[1em] \Rightarrow 2y = \dfrac{x}{3} - 4 \\[1em] \Rightarrow y = \dfrac{1}{6}x - 2.$

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

Slope = $\dfrac{1}{6}$.

Let slope of perpendicular line be m.

Since, product of slopes of perpendicular lines = -1.

∴ m × $\dfrac{1}{6}$ = -1

⇒ m = -6.

Hence, slope of the line perpendicular to the line $\dfrac{x}{3} - 2y = 4$ is -6.