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.