Question

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

• A. x + y - 5 = 0
• B. x + y + 1 = 0
• C. x + y - 1 = 0
• D. x + y + 5 = 0

Answer 1

The correct option is A

x + y - 5 = 0

Here, m = slope of a line

We know, m = tan ${135}^{\circ }$ = tan(${90}^{\circ }$ + ${45}^{\circ }$) = - cot ${45}^{\circ }$ = - 1

So, equation of the line is

$y-y_1=m(x-x_1)$

and $(x_1,y_1)$ $\Rightarrow$ (2, 3)

y - 3 = -1(x - 2)

y - 3 = - x + 2

x + y - 5 = 0

So, equation of the line is x + y - 5 = 0