Graphing Linear Inequalities in Two Variables

To graph y < 2x + 3 (or leq, >, geq): Step 1: Draw the boundary line — graph y = 2x + 3. - Dashed line for < or > (boundary NOT included) - Solid line for leq or geq (boundary included) Step 2: Shade the correct side. - For y < or y leq: shade below the line - For y > or y geq: shade above the line Shortcut: if the inequality is solved for y: - y < ... → shade below - y > ... → shade above

If you're unsure which side to shade: 1. Pick a test point not on the line ((0, 0) is easiest if the line doesn't pass through the origin) 2. Substitute into the inequality 3. If the result is true: shade the side containing that point 4. If false: shade the other side

Example: Determine which side of 2x + y > 6 contains the solutions.