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Systems of Linear Inequalities Graphing Solver

Systems of Linear Inequalities Graphing Solver
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2012-08-08 02:06
FunctionCoordinate GeometryInequalityGraphing
This GeoGebra applet demonstrates the graphical solution of systems of linear inequalities in the coordinate plane, showing how the intersection of half-planes bounded by two lines forms the feasible region of the inequality system. Core mathematical concepts include linear inequalities, systems of inequalities, boundary lines, shaded solution regions, feasible sets, and the connection between algebraic expressions and geometric graphs. The construction relies on GeoGebra objects m, b, a, c and m₁, b₁ to define line slopes and intercepts, auxiliary variables d, e, f, g, h, i to manage inequality conditions, text objects text1, text2, text3, text5 for labeling, and point A together with region objects j, k, l, n, o, p, q, r to shade and dynamically display the overlapping solution area. It is designed for middle school algebra (grades 7–9) and high school review, supporting classroom teaching and interactive student exploration of inequality systems.

GeoGebra Commands & Parameters

  1. Numeric m(-1.59)
  2. Numeric b(0.32)
  3. y ≥ m * x + b
  4. y ≤ m * x + b
  5. Numeric m_1(3.36)
  6. Numeric b_1(-0.64)
  7. Boolean d(false)
  8. Boolean e(false)
  9. y ≥ m_1 * x + b_1
  10. Boolean g(false)
  11. y ≤ m_1 * x + b_1
  12. Boolean i(false)
  13. y < m * x + b
  14. Boolean k(false)
  15. y > m * x + b
  16. Boolean n(false)
  17. y < m_1 * x + b_1
  18. Boolean p(false)
  19. y > m_1 * x + b_1
  20. Boolean r(false)
  21. Point A(4.23604747304451, 5.458050319710121)

AI Drawing Prompt Reference

Draw two lines in a coordinate plane, one dashed and one solid, representing two linear inequalities. Shade the regions between and outside the lines according to the inequalities, showing the solution sets. Mark the intersection point of the lines and label the inequalities and solution regions.
The prompt above was compiled from the original drawing commands and is for reference only.