If 6x + 5y - 7 = 0 and 2px + 5y + 1 = 0 are parallel lines, find the value of p.

Converting 6x + 5y - 7 = 0 in the form y = mx + c we get,

⇒ 6x + 5y - 7 = 0

⇒ 5y = -6x + 7

⇒ y = $-\dfrac{6}{5}x + \dfrac{7}{5}$

Comparing, we get slope of this line = m₁ = $-\dfrac{6}{5}$.

Converting 2px + 5y + 1 = 0 in the form y = mx + c we get,

⇒ 2px + 5y + 1 = 0

⇒ 5y = -2px - 1

⇒ y = $-\dfrac{2p}{5}x - \dfrac{1}{5}$

Comparing, we get slope of this line = m₂ = $-\dfrac{2p}{5}$

Given, two lines are parallel so their slopes will be equal,

m₁ = m₂

$\Rightarrow -\dfrac{6}{5} = -\dfrac{2p}{5} \\[1em] \Rightarrow 2p = 6 \\[1em] \Rightarrow p = 3.$

Hence, the value of p = 3.