For the given rectangular equation, give its equivalent polar equation.
-$6 x - y = 14$
A) $r = \frac { 14 } { 6 \sin \theta - \cos \theta }$

B) $r = \frac { 14 } { 6 \cos \theta - \sin \theta }$

C) $r = \frac { 6 } { 14 \cos \theta - \sin \theta }$

D) $r = \frac { 14 } { 6 \cos \theta + \sin \theta }$

Question

For the given rectangular equation, give its equivalent polar equation.
-$6 x - y = 14$
A) $r = \frac { 14 } { 6 \sin \theta - \cos \theta }$

B) $r = \frac { 14 } { 6 \cos \theta - \sin \theta }$

C) $r = \frac { 6 } { 14 \cos \theta - \sin \theta }$

D) $r = \frac { 14 } { 6 \cos \theta + \sin \theta }$

Quizplus · Accepted Answer

To convert the rectangular equation $6x - y = 14$ to polar form, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $6r\cos\theta - r\sin\theta = 14$, which simplifies to $r = \frac{14}{6\cos\theta - \sin\theta}$, matching option B.

For the Given Rectangular Equation, Give Its Equivalent Polar Equation 6x−y=146 x - y = 146x−y=14

For the Given Rectangular Equation, Give Its Equivalent Polar Equation $6 x - y = 14$