The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).
-$$2 x + 3 y = 6$$
A) $2 \sin \theta + 3 \cos \theta = 6 r$
B) $2 \cos \theta + 3 \sin \theta = 6 r$
C) $\mathrm { r } ( 2 \cos \theta + 3 \sin \theta ) = 6$
D) $r ( 2 \sin \theta + 3 \cos \theta ) = 6$

Question

Quizplus · Accepted Answer

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

The Letters X and Y Represent Rectangular Coordinates 2x+3y=62 x + 3 y = 62x+3y=6

The Letters X and Y Represent Rectangular Coordinates $2 x + 3 y = 6$