Question:
The graph of the inequation \( 2x + 3y>6 \) is the:
The graph of the inequation \( 2x + 3y>6 \) is the:
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For linear inequalities, test a point (e.g., the origin) to determine which half-plane satisfies the inequality.
Updated On: Jan 13, 2026
- Entire XOY-plane
- Half-plane that contains the origin
- Half-plane that neither contains the origin nor the points on the line \( 2x + 3y = 6 \)
- Whole XOY-plane excluding the points on the line \( 2x + 3y = 6 \)
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The Correct Option is C
Solution and Explanation
Step 1: Rewrite the inequality: \[ 2x + 3y>6 \quad \Rightarrow \quad y>-\frac{2}{3}x + 2. \] Step 2: The inequality represents the region above the line \( 2x + 3y = 6 \), excluding the points on the line.
Since \( 2(0) + 3(0) = 0 \not > 6 \), the origin is not part of the solution.
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