Answer
$y = -\frac{\sqrt 3}{3} x$
See graph below
Work Step by Step
The question asks for a graph of the polar equation and to convert the equation into rectangular coordinates
Given $θ = \frac{5\pi}{6}$
The graph consists of all points of which the θ-coordinate is $\frac{5\pi}{6}$, which is a line that passes through the origin and makes the angle of $\frac{5\pi}{6}$ relative to the polar axis. See graph below.
To convert the equation into rectangular coordinates, the following equation can be used:
$\tan θ = \frac{y}{x}$
So $θ = \frac{5\pi}{6}$
$\tan θ = \tan \frac{5\pi}{6}$
$\frac{y}{x} = -\frac{\sqrt 3}{3}$
$y = -\frac{\sqrt 3}{3} x$
