Find the equation of a line passing through $(2, - 3)$ and inclined at an angle of $135^{o}$ with the positive direction of x axis

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Solution

Here m = slope of the line = $tan 135^{\circ} = tan (90^{\circ} + 45^{\circ}) = - cot 45^{\circ} = - 1, x_{1} = 2, y_{1} = - 3$
So the equation of the line is $y - y_{1} = m (x - x_{1})$
i.e. $y - (- 3) = - 1 (x - 2)$ or $y + 3 = - x + 2$ or $x + y + 1 = 0$

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