Rewriting a Cartesian Equation in Polar Form

Rewrite the Cartesian equation $y = 3 x + 2$ as a polar equation.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We will use the relationships $x = r \cos θ$ and $y = r \sin θ .$
$\begin{array}{l} y = 3 x + 2 \\ r \sin θ = 3 r \cos θ + 2 \\ r \sin θ - 3 r \cos θ = 2 \\ r (\sin θ - 3 \cos θ) = 2 & Isolate r . \\ r = \frac{2}{\sin θ - 3 \cos θ} \begin{matrix} \end{matrix} & Solve for r . \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Rewrite the Cartesian equation $y^{2} = 3 - x^{2}$ in polar form.

How did it go?