The equation of a line passing through the origin and perpendicular to the line
7x - 3y + 4 = 0 is:

7x - 3y + 4 = 0

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3x + 7y = 0

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3x - 7y + 4 = 0

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7x - 3y = 0

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Solution

The correct option is B
3x + 7y = 0

$F o r l i n e w i t h e q u a t i o n a x + b y + c = 0 t h e s l o p e i s (- a) / b C o m p a r i n g t h e g i v e n e q u a t i o n 7 x - 3 y + 4 = 0, a = 7; b = - 3 S l o p e o f t h e l i n e 7 x - 3 y + 4 = 0 i s (- 7) / (- 3) \Rightarrow m_{1} = 7 / 3 W e k n o w t h a t t h e p r o d u c t o f s l o p e o f t w o p e r p e r p e n d i c u l a r l i n e s a r e - 1 m_{1} \times m_{2} = - 1 S l o p e o f t h e l i n e p e r p e n d i c u l a r t o 7 x - 3 y + 4 = 0 i s m_{2} = (- 1) / (7 / 3) = (- 3) / 7 H e r e t h e p a s s i n g t h r o u g h p o i n t i s O r i g i n O (0, 0) A p p l y i n g o n e p o i n t s l o p e f o r m, T h e e q u a t i o n o f r e q u i r e d l i n e i s y - 0 = (- 3) / 7 (x - 0) 3 x + 7 y = 0$

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