The equation of the line passing through the above given points is

3 x - y + 13 = 0

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3 x + y - 13 = 0

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x + 3 y - 13 = 0

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x - 3 y + 13 = 0

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Solution

The correct option is B $3 x + y - 13 = 0$
$E q u a t i o n o f t h e s t r a i g h t l i n e p a s s i n g t h r o u g h p o i n t s (x_{1}, y_{1}) a n d (x_{2}, y_{2}) i s y - y_{1} = \frac{x - x_{1}}{x_{2} - x_{1}} (y_{2} - y_{1}) H e r e (x_{1}, y_{1}) = (4, 1) a n d (x_{2}, y_{2}) = (5, - 2) ∴ T h e r e q u i r e d e q a t i o n i s y - 1 = \frac{x - 4}{5 - 4} (- 2 - 1) ⟹ - 3 x + 12 = y - 1 ⟹ 3 x + y - 13 = 0 A n s - O p t i o n B$

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The equation of the line passing through the above given points is

The correct option is B 3x+y−13=0Equationofthestraightlinepassingthroughpoints(x1,y1)and(x2,y2)isy−y1=x−x1x2−x1(y2−y1)Here(x1,y1)=(4,1)and(x2,y2)=(5,−2)∴Therequiredeqationisy−1=x−45−4(−2−1)⟹−3x+12=y−1⟹3x+y−13=0Ans−Option B