Question

A straight line makes an angle of $135°$ with the x-axis and cuts y-axis at a distance $-5$ from the origin. The equation of the line is

• A. $2x+y+5=0$
• B. $x+2y+3=0$
• C. $x+y+5=0$
• D. $x+y+3=0$

Answer 1

The correct option is C

$x+y+5=0$

Explanation for the correct answer:

Step 1: Finding the slope.

Let $\theta$ be the angle of straight line with the x-axis, so slope $m=\tan (135°)$

$$\begin{gathered} \Rightarrow m=\tan \left(135\right) \\ =\tan \left(90+45\right) \\ =-1...\left[\because \tan \left(135\right)liesin2ndquadrant\right] \end{gathered}$$

The straight line cuts the y-axis at $-5$. So y-intercept is $c=-5$

Step 2: Finding the equation of line.

The formula to find equation of line with slope - intercept form is

$y=mx+c$

On substituting the above values,

$$\begin{gathered} \Rightarrow y=(-1)x+(-5) \\ \Rightarrow y=-x-5 \\ \Rightarrow x+y+5=0 \end{gathered}$$

Hence, option (C) $\mathit{x}\mathbf{+}\mathit{y}\mathbf{+}\mathbf{5}\mathbf{=}\mathbf{0}$ is the correct answer.