Chapter 13.7, Problem 32WE

To determine

To find : an equation of line described

Answer to Problem 32WE

The equation is $x+y=0$

Explanation of Solution

Given information :

The line through the origin that’s makes an $135°$ angle measured counterclockwise from the positive $x$ -axis

Formula used :

  $y-y_1=m\left(x-x_1\right)$

Calculation :

Let $\theta =135°$

The slope

  $\begin{array}{l}\tan \theta \\ =\tan 135°\\ =-1\end{array}$

Therefore, the slope is $-1$ .

The origin means the point $\left(0,0\right)$

Using $\left(0,0\right)$ , the equation is

  $\begin{array}{l}y-0=-1\left(x-0\right)\\ y=-x+0\\ x+y=0\end{array}$

Hence, the equation is $x+y=0$ .