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Exploring Linear Equations, Systems, and Inequalities with Sliders

Exploring Linear Equations, Systems, and Inequalities with Sliders
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2012-06-14 07:50
FunctionCoordinate GeometryInequalitySlider AnimationGraphing
In collections Systems of Equations and Inequalities
This GeoGebra example allows users to investigate linear equations, systems of linear equations, and linear inequalities. By adjusting slope, intercept, and shading via sliders, learners can visualize solution sets and understand the relationship between algebraic expressions and their graphical representations. The construction uses GeoGebra commands such as Line, Circle, Polygon, Text, Semicircle, and Point, along with objects like shada, poly1, inta, etc. It is designed for high‑school algebra and introductory coordinate geometry courses.

GeoGebra Commands & Parameters

  1. Circle(A, 30) → c
  2. Polygon(B, C, D, E) → poly1, b_1, c_1, d, e
  3. Text("Equation 1") → text1
  4. Semicircle(Point[First[inta]], Point[Last[inta]]) → semia1
  5. Semicircle(Point[Last[inta]], Point[First[inta]]) → semia2
  6. Polygon(F, G, H, I) → poly2, f_1, g, h, i
  7. Text("Equation 2") → text2
  8. Semicircle(Point[First[intb]], Point[Last[intb]]) → semib1
  9. Semicircle(Point[Last[intb]], Point[First[intb]]) → semib2
  10. Text("y > " + m1 + "x +" + b1) → text3
  11. Text("y < " + m1 + "x +" + b1) → text4
  12. Text("y ≥ " + m1 + "x +" + b1) → text5
  13. Text("y ≤ " + m1 + "x +" + b1) → text6
  14. Text("y > " + m2 + "x +" + b2) → text8
  15. Text("Eq 1:") → text7
  16. Text("y < " + m2 + "x +" + b2) → text9
  17. Text("y ≥ " + m2 + "x +" + b2) → text10
  18. Text("y ≤ " + m2 + "x +" + b2) → text11
  19. Text("Eq 2:") → text12
  20. Text(If[y(Eq1_{sol}) ≥ m1 * x(Eq1_{sol}) + b1, "Solution", "Not Solution"]) → text15
  21. Text(If[y(Eq1_{sol}) ≤ m1 * x(Eq1_{sol}) + b1, "Solution", "Not Solution"]) → text16
  22. Text(If[y(Eq1_{sol}) > m1 * x(Eq1_{sol}) + b1, "Solution", If[y(Eq1_{sol}) < m1 * x(Eq1_{sol}) + b1, "Not Solution", "y = " + m1 + "x + " + b1 + " Not Solution"]]) → text13
  23. Text(If[y(Eq1_{sol}) < m1 * x(Eq1_{sol}) + b1, "Solution", If[y(Eq1_{sol}) > m1 * x(Eq1_{sol}) + b1, "Not Solution", "y = " + m1 + "x + " + b1 + " Not Solution"]]) → text14
  24. Text(If[y(Eq2_{sol}) > m2 * x(Eq2_{sol}) + b2, "Solution", If[y(Eq2_{sol}) < m2 * x(Eq2_{sol}) + b2, "Not Solution", "y = " + m2 + "x + " + b2 + " Not Solution"]]) → text17
  25. Text(If[y(Eq2_{sol}) < m2 * x(Eq2_{sol}) + b2, "Solution", If[y(Eq2_{sol}) > m2 * x(Eq2_{sol}) + b2, "Not Solution", "y = " + m2 + "x + " + b2 + " Not Solution"]]) → text18
  26. Text(If[y(Eq2_{sol}) ≥ m2 * x(Eq2_{sol}) + b2, "Solution", "Not Solution"]) → text19
  27. Text(If[y(Eq2_{sol}) ≤ m2 * x(Eq2_{sol}) + b2, "Solution", "Not Solution"]) → text20
  28. Line(S2, S1) → s
  29. Point(s) → K1
  30. Text("y = " + (y(K1)) + (If[y(K1) < t, "<", If[y(K1) > t, ">", "="]]) + m1 + "*" + (x(K1)) + "+" + b1 + " = " + t) → text21
  31. Text(If[(y(System_{sol}) > m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) > m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text22
  32. Text(If[(y(System_{sol}) > m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) < m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text23
  33. Text(If[(y(System_{sol}) > m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≥ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text24
  34. Text(If[(y(System_{sol}) > m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≤ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text25
  35. Text(If[(y(System_{sol}) < m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) > m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text26
  36. Text(If[(y(System_{sol}) < m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) < m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text27
  37. Text(If[(y(System_{sol}) < m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≥ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text28
  38. Text(If[(y(System_{sol}) < m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≤ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text29
  39. Text(If[(y(System_{sol}) ≥ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≤ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text30
  40. Text(If[(y(System_{sol}) ≥ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≥ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text31
  41. Text(If[(y(System_{sol}) ≥ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) < m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text32
  42. Text(If[(y(System_{sol}) ≥ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) > m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text33
  43. Text(If[(y(System_{sol}) ≤ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) > m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text34
  44. Text(If[(y(System_{sol}) ≤ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) < m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text35
  45. Text(If[(y(System_{sol}) ≤ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≥ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text36
  46. Text(If[(y(System_{sol}) ≤ m1 * x(System_{sol}) + b1) ∧ (y(System_{sol}) ≤ m2 * x(System_{sol}) + b2), "Solution", " Not Solution"]) → text37
  47. Text("y = " + m1 + "x +" + b1) → text41
  48. Text("y = " + m2 + "x +" + b2) → text42

AI Drawing Prompt Reference

Draw two lines with adjustable slopes and intercepts using sliders, and represent their solution sets for inequalities (>, <, ≥, ≤) with different colors and styles. Label each line with its equation and inequality type, fill the solution regions with distinct colors in the coordinate system, and mark the system solution on the lines.
The prompt above was compiled from the original drawing commands and is for reference only.