Find the slope of the line which is perpendicular to $x - \dfrac{y}{2} + 3 = 0$.

Given,

$\Rightarrow x - \dfrac{y}{2} + 3 = 0 \\[1em] \Rightarrow \dfrac{y}{2} = x + 3 \\[1em] \Rightarrow y = 2x + 6.$

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

Slope = 2.

Let slope of perpendicular line be m.

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

∴ m × 2 = -1

⇒ m = $-\dfrac{1}{2}$.

Hence, slope of the line perpendicular to the line $x - \dfrac{y}{2} + 3 = 0 \text{ is } -\dfrac{1}{2}.$