Answer
The graph is a line with slope $\dfrac{-1}{\sqrt 3}$ and y-intercept $\dfrac{4}{\sqrt 3}$.
Work Step by Step
Conversion of polar coordinates and Cartesian coordinates are as follows:
a) $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
c) $x=r \cos \theta$
d) $y=r \sin \theta$
Here, we have $r^2=\dfrac{\sqrt 3}{2}r \sin \theta+\dfrac{1}{2}r \cos \theta $
Therefore, our Cartesian equation is $y=\dfrac{-1}{\sqrt 3}x+\dfrac{4}{\sqrt 3}$
This shows that the graph is a line with slope $\dfrac{-1}{\sqrt 3}$ and y-intercept $\dfrac{4}{\sqrt 3}$.
