Recording-2025-02-05T21:54:24.473Z

Understanding Test Points and Shading

• Test Points

  • When graphing inequalities, the objective is to determine which side of the line to shade based on a test point.

  • Example Test Point: (0, 0)

  • If substituting the test point results in a true statement, shade the side that includes this point.

  • If it results in a false statement, shade the opposite side.

Shading Techniques

• When prompted with a "yes" or "no" for a test point, interpret:

  • "Yes" means that the point satisfies the inequality, shade that side.

  • "No" means the point does not satisfy the inequality, shade the opposite side.

  • Ensure your shading corresponds accurately to the reference point's location.

System of Equations and Unique Solutions

• Intersection of Lines

  • A unique solution for a system of equations occurs where two lines intersect.

  • Identify which lines intersect at specific points when solving these systems.

  • Example: Points labeled as A, B, and C can help locate intersection points in a graphical representation.

Solving Inequalities

• Approach to Finding Coordinates

  • Given multiple inequalities, such as:

    • 2v + 1m ≤ 500

    • 3v + 3m ≥ 900

  • Substitute values for easy coordinates, for example, setting v = 0 to find y values.

  • Determine the corner points of the feasible region by identifying intersection points.

Choosing Corner Points

• Color Coding and Feasible Regions

  • Use visual cues (such as colored points) to signify corners of the feasible region.

  • Focus on picking corner points that are closest to the usable area of the graph, avoiding points that are distant from the core region of interest.