The equation of the line passing through (1, - 5) and making an angle $135^{\circ}$ with the x-axis is

x - y + 4 = 0

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x - y - 4 = 0

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x + y - 2 = 0

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x + y + 4 = 0

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Solution

The correct option is D $x + y + 4 = 0$
Equation of a line passing through $(x_{1}, y_{1})$ having slope $m = tan θ$ is
$y - y_{1} = m (x - x_{1})$
Equation of a line passing through $(1, - 5)$ having slope $m = tan 135^{\circ} = tan (90 + 45) = - cot 45^{\circ} = - 1$ is
$y + 5 = - 1 (x - 1)$
$\Rightarrow y + 5 + x - 1 = 0$ or $x + y + 4 = 0$
$∴ x + y + 4 = 0$ required equation.

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The equation of the line passing through (1, - 5) and making an angle 135∘ with the x-axis is

The correct option is D x+y+4=0Equation of a line passing through (x1,y1) having slope m=tanθ isy−y1=m(x−x1)Equation of a line passing through (1,−5) having slope m=tan135∘=tan(90+45)=−cot45∘=−1 isy+5=−1(x−1)⇒y+5+x−1=0 or x+y+4=0∴x+y+4=0 required equation.

The equation of the line passing through (1, - 5) and making an angle $135^{\circ}$ with the x-axis is