What is the equation of a line which makes an angle of $135°$ with the positive direction of $X$-axis and passes through the point $(3,5)$?

 

Let the equation of the straight line be $y=mx+c.$

Given the slope of the line, $m=\tan 135°=-1$.

Now the equation of the straight line becomes $y=x(-1)+c\Rightarrow y=-x+c.$

And the straight line passes through the point $(3,5).$

$\therefore$The point has to satisfy the straight line.

$$\begin{gathered} \Rightarrow 5=-3+c \\ \Rightarrow c=8 \end{gathered}$$

$\therefore$ The required equation of the line is $y=-x+8.$

Thus the equation of the line which makes an angle of ${135}^{°}$ with the positive direction of $X$-axis and passes through the point $\left(3,5\right)$ is $x+y=8$.

Therefore, the correct option is $1$.