Find the value of $k$ so that the line $2 x - k y - 7 = 0$ may be parallel to $3 x + 4 y + 7 = 0$

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Solution

Given: $2 x - k y - 9 = 0$ ....... $(1)$
Slope of line $(1) = - \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = - \frac{2}{- k} = \frac{2}{k}$
Given: $3 x + 4 y + 7 = 0$ ....... $(2)$
Slope of line $(2) = - \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = - \frac{3}{4} = \frac{- 3}{4}$
As the lines $(1)$ and $(2)$ are parallel, $\frac{2}{k} = \frac{- 3}{4}$
$\Rightarrow 8 = - 3 k$
$\Rightarrow k = \frac{- 8}{3}$

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