The lines represented by 4x + 3y = 9 and px – 6y + 3 = 0 are parallel. Find the value of p.

Given lines,

⇒ 4x + 3y = 9 and px - 6y + 3 = 0

⇒ 3y = -4x + 9 and 6y = px + 3

⇒ y = $-\dfrac{4}{3}x + 3$ and $y = \dfrac{p}{6}x + \dfrac{1}{2}$

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

Slope of 1st line = $-\dfrac{4}{3}$

Slope of 2nd line = $\dfrac{p}{6}$

Since,

Slopes of parallel lines are equal.

$\therefore -\dfrac{4}{3} = \dfrac{p}{6} \\[1em] \Rightarrow p = \dfrac{-4 \times 6}{3} \\[1em] \Rightarrow p = -8.$

Hence, p = -8.