Answer
$\theta=\pi/4.$
Work Step by Step
Conversion formulas: $\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
From this line equation, or, $\qquad y=x,\quad$ we see that:
- it passes through the origin
- the slope is 1 (that is, $\tan\theta=1$)
The whole line is included, (both sides of the pole) so we allow r to be negative.
In fact, r can be any number, and $\theta$ can be $\pi/4$, as $\tan(\pi/4)=1$
Thus, a polar equation for this line is
$\theta=\pi/4.$
