Find the equation of the line perpendicular to the line $3 x + 4 y + 6 = 0$ and making an intercept $- 4$ on the $X -$ axis.

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Solution

Slope of $3 x + 4 y + 6 = 0$ ,
$m_{1} = \frac{- 3}{4}$
Let slope of required line be $m_{2}$
As the two lines are perpendicular $\Rightarrow m_{1} m_{2} = - 1$
$\Rightarrow m_{2} = \frac{4}{3}$
and the line passes through $(- 4, 0)$
$\Rightarrow$ Its equation: $y = 0 = \frac{4}{3} (x + 4)$
$\Rightarrow 3 y = 4 x + 16$ .

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