Lines 2x – by + 5 = 0 and ax + 3y = 2 are parallel to each other. Find the relation connecting a and b.

Given lines,

⇒ 2x – by + 5 = 0 and ax + 3y = 2

⇒ by = 2x + 5 and 3y = -ax + 2

⇒ y = $\dfrac{2}{b}x + \dfrac{5}{2}$ and $y = -\dfrac{a}{3}x + \dfrac{2}{3}$

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

Slope of 1st line = $\dfrac{2}{b}$

Slope of 2nd line = $-\dfrac{a}{3}$

Since,

Slopes of parallel lines are equal.

$\therefore \dfrac{2}{b} = -\dfrac{a}{3} \\[1em] \Rightarrow 6 = -ab \\[1em] \Rightarrow ab = -6.$

Hence, relation connecting a and b is ab = -6.