(1 point) A curve with polar equation
\[
r=\frac{3}{6 \sin \theta+37 \cos \theta}
\]
represents a line.
Write this line in the given Cartesian form.
\[
y=
\]
( Note: Your answer should be a function of $x$.)
Answer
Thus, the line in Cartesian form is \(\boxed{y=0.5 - 6.16666666666667x}\).
Step 1 ：Given the polar equation \(r=\frac{3}{6 \sin \theta+37 \cos \theta}\), we want to convert this to Cartesian form.
Step 2 ：We know that in polar coordinates, \(x = r\cos(\theta)\) and \(y = r\sin(\theta)\).
Step 3 ：Substituting these into the given equation, we get \((x^2 + y^2)^{0.5} - \frac{3}{37\frac{x}{\sqrt{x^2 + y^2}} + 6\frac{y}{\sqrt{x^2 + y^2}}}\).
Step 4 ：Solving this equation for \(y\) in terms of \(x\), we find that \(y = 0.5 - 6.16666666666667x\).
Step 5 ：Thus, the line in Cartesian form is \(\boxed{y=0.5 - 6.16666666666667x}\).
