The equation of the line passing through $(1, 5)$ and perpendicular to the line $3 x - 5 y + 7 = 0$ is

$5 x + 3 y - 20 = 0$

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$3 x - 5 y + 7 = 0$

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$3 x - 5 y + 6 = 0$

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$5 x + 3 y + 7 = 0$

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Solution

The correct option is A
$5 x + 3 y - 20 = 0$

A line perpendicular to $3 x - 5 y + 7 = 0$ is given by

$5 x + 3 y + λ = 0$

This line passes through $(1, 5)$

$5 + 15 + λ = 0$

$\Rightarrow λ = - 20$

Therefore, the equation of the required line is $5 x + 3 y - 20 = 0$

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