Find the equation to that straight line passing through (1,2) and parallel to $x - 3 y - 22 = 0$ .

x - 3 y + 5 = 0

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x - 3 y + 12 = 0

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x-3y=23$

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None

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Solution

The correct option is A $x - 3 y + 5 = 0$
$f o r m u l a used$
$equation of line passing through (x_{1}, y_{1})$
$y - y_{1} = m (x - x_{1})$
$G i v e n$
$e q u a t i o n o f l i n e$
$x - 3 y - 22 = 0$
$\Rightarrow 3 y = x - 22$
$\Rightarrow y = \frac{x}{3} - \frac{22}{3}$
$c o m p a r i n g w i t h y = m x + c$
$m = \frac{1}{3}$
$sin c e t h e l i n e i s p a r a l l e l h e n c e t h e s l o p e i s s a m e$
$e q u a t i o n o f l i n e p a s sin g t h r o u g h (1, 2) w i t h s l o p e \frac{1}{3} i s$
$y - 2 = \frac{1}{3} (x - 1)$
$\Rightarrow 3 y - 6 = x - 1$
$\Rightarrow x - 3 y + 5 = 0$

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