Replace the Cartesian equation with an equivalent polar equation.
-2x + 3y = 6
A) $2 \sin \theta + 3 \cos \theta = 6 r$
B) $2 \cos \theta + 3 \sin \theta = 6 r$
C) $\mathrm { r } ( 2 \sin \theta + 3 \cos \theta ) = 6$
D) $r ( 2 \cos \theta + 3 \sin \theta ) = 6$

Question

Replace the Cartesian equation with an equivalent polar equation.
-2x + 3y = 6 
A) $2 \sin \theta + 3 \cos \theta = 6 r$
B) $2 \cos \theta + 3 \sin \theta = 6 r$
C) $\mathrm { r } ( 2 \sin \theta + 3 \cos \theta ) = 6$
D) $r ( 2 \cos \theta + 3 \sin \theta ) = 6$

Quizplus · Accepted Answer

To convert the Cartesian equation $2x + 3y = 6$ to a polar equation, use the relationships $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the given equation yields $2(r \cos \theta) + 3(r \sin \theta) = 6$, which simplifies to $r(2 \cos \theta + 3 \sin \theta) = 6$.

Replace the Cartesian Equation with an Equivalent Polar Equation 2sin⁡θ+3cos⁡θ=6r2 \sin \theta + 3 \cos \theta = 6 r2sinθ+3cosθ=6r

Replace the Cartesian Equation with an Equivalent Polar Equation $2 \sin \theta + 3 \cos \theta = 6 r$