For the Given Rectangular Equation, Give Its Equivalent Polar Equation $$2 x + 3 y = 6$$

question 22

Multiple Choice

For the given rectangular equation, give its equivalent polar equation.
- $$2 x + 3 y = 6$$

• A) \(r = \frac { 6 } { 2 \sin \theta + 3 \cos \theta }\)
• B) \(r = \frac { 2 \cos \theta + 3 \sin \theta } { 6 }\)
• C) \(r = \frac { 6 } { 2 \cos \theta + 3 \sin \theta }\)
• D) \(r = \frac { 2 \sin \theta + 3 \cos \theta } { 6 }\)

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Definitions:

Standard Form

A way of structuring arguments, statements, or equations according to established rules to make them clearer, easier to analyze, or solve.

Hypothetical Syllogism

A logical argument consisting of two conditional premises and a conclusion, based on if-then scenarios.

Modus Ponens

A valid form of argument in which if a conditional statement ("if P then Q") is accepted, and P is asserted to be true, then Q necessarily follows.

Modus Tollens

A logical argument form where the contrapositive of a premise is used to infer the negation of the hypothesis.