The solution region of the inequality 2x+4y ≤ 9 is:

The correct answer is Option (2) → closed half plane containing origin

This equation represents a straight line in the $xy$-plane. The inequality includes the "equal to" part ($\le$), which means the line itself is part of the solution region. This tells us that the solution region will be a closed half-plane. Further, the origin satisfies the inequality.

Note: The inequality 2x+4y≤9 represents a closed half-plane. 2x+4y=9 is included in the solution. Therefore, since the line is included here, the solution represents a closed half-plane.