Find the value of $k$ so that the line $x + k y - 4 = 0$ may be parallel to $5 x + 3 y - 2 = 0$

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Solution

Given: $x + k y - 4 = 0$ ....... $(1)$
Slope of line $(1) = - \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = - \frac{1}{k} = \frac{- 1}{k}$
Given: $5 x + 3 y - 2 = 0$ ....... $(2)$
Slope of line $(2) = - \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = - \frac{5}{3}$
As the lines $(1)$ and $(2)$ are parallel, $\frac{- 1}{k} = \frac{- 5}{3}$
$\Rightarrow k = \frac{3}{5}$
$\Rightarrow k = \frac{3}{5}$

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