[Math] Polar coordinate line to slope intercept form

Question

I'm finding it very difficult to find an answer on google and in my math book on this. The question give to us is:

A curve with polar equation

$$
r= \frac{39}{9\sin\theta+19\cos\theta}
$$

represents a line. This line has a Cartesian equation of the form
$y = mx + b$, where $m$ and $b$ are constants. Give the formula
for $y$ in terms of $x$. For example, if the line had equation
$y = 2x+3$ then the answer would be $2x + 3$.

I have tried to take the derivative of this equation to get $m$ and I have plugged in $0$ for $\theta$ in an attempt to get $b$. I originally did this by trying to convert $r$ to cartesian coordinates first by using $x = r\sin\theta$ and $y = r\cos\theta$, but with no success. We never covered this in class and I can't find any examples anywhere that have helped me answer this. Is there a process to follow when converting the entire equation from polar curves to cartesian equations?

Thank you!

Answer 1

Hint: $$9r\sin\theta+19r\cos\theta=39\ .$$