Answer
The graph is a line with slope $\dfrac{-1}{\sqrt 3}$ and y-intercept is $\dfrac{4}{\sqrt 3}$.
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
3. $x=r \cos \theta$ and 4. $y=r \sin \theta$
Given: $r^2=\dfrac{\sqrt 3}{2}r \sin \theta+\dfrac{1}{2}r \cos \theta $
Thus, the Cartesian equation is $y=(\dfrac{-1}{\sqrt 3})x+(\dfrac{4}{\sqrt 3})$
Hence, this shows that the graph is a line with slope $\dfrac{-1}{\sqrt 3}$ and y-intercept is $\dfrac{4}{\sqrt 3}$.
