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Graph -2x - 2y > -6. Upload a clear picture. - Show at least two points on the boundary - Use the correct...

Graph -2x - 2y > -6.
Upload a clear picture.
- Show at least two points on the boundary
- Use the correct boundary style (dotted line or solid line)
- Shade the solution region.
- Include a labeled test point explaining your shading choice.

Answer

Graph -2x - 2y > -6:

  1. Equation of the boundary line: Convert the inequality to an equation: -2x - 2y = -6. Simplify to y = -x + 3.
  2. Boundary points: Choose two points on the line y = -x + 3, such as (0, 3) and (3, 0).
  3. Boundary style: Since the inequality is '>', use a dotted line to indicate that points on the line are not included in the solution.
  4. Shading the solution region: Test a point not on the line, such as (0, 0). Substitute into the inequality: -2(0) - 2(0) > -6, which simplifies to 0 > -6 (true). Shade the region containing (0, 0).
  5. Labeled test point: Use (0, 0) as the test point, and label it on the graph to show why the region is shaded.

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