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To solve this, we need to convert the given Cartesian equation \( 2x + 3y = 6 \) into polar coordinates.

Recall the relationships between Cartesian and polar coordinates:
\[
x = r \cos \theta
\]
\[
y = r \sin \theta
\]

We substitute these into the original equation \( 2x + 3y = 6 \):

\[
2(r \cos \theta) + 3(r \sin \theta) = 6
\]
\[
r(2 \cos \theta + 3 \sin \theta) = 6
\]

Thus, the equation in polar form becomes:
\[
r(2 \cos \theta + 3 \sin \theta) = 6
\]

This matches option **c**.

Would you like further details on the conversion process or clarifications?

Here are some related questions for practice:

1. How do you convert an equation from Cartesian to polar coordinates?
2. What are the relationships between \(x, y\) and \(r, \theta\) in polar coordinates?
3. How can we find the radius \(r\) in polar coordinates from a given point \((x, y)\)?
4. Can any Cartesian equation be converted to polar form?
5. What are the advantages of using polar coordinates in specific types of problems?

**Tip**: Always check the substitution carefully when converting between coordinate systems to avoid common mistakes.

Find an equation equivalent to 2x + 3y = 6 in polar coordinates.

This page covers the step-by-step process of converting the Cartesian equation 2x + 3y = 6 to its equivalent polar coordinate form. Learn key concepts like the relationship between Cartesian and polar coordinates using r, cos(θ), and sin(θ). Suitable for high school students in Grades 10-12.

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