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线性方程与不等式系统 - 探索与可视化

线性方程与不等式系统 - 探索与可视化
几何画板及绘图内容加载中，请稍等……
2012-06-14 07:50
函数解析几何不等式滑块动画函数图像
所属专题 Systems of Equations and Inequalities
本示例展示了线性方程、线性方程组和线性不等式的可视化探索。通过滑块调节斜率、截距和阴影区域，学生可以直观地观察解集的变化。核心数学概念包括一次函数的图象、方程组的交点解、不等式区域的表示。GeoGebra 中使用了直线（Line）、圆形（Circle）、多边形（Polygon）、文本（Text）、半圆（Semicircle）和点（Point）等命令，以及多个对象（如 shada, poly1, inta 等）来构建交互界面。适合高中 algebra 和初等解析几何课程使用。

GeoGebra 命令及参数

  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 绘图提示语参考

画两条直线和它们的系统解，每条直线用滑块控制斜率和截距，并用不同颜色和样式表示不等式的解集，包括大于、小于、大于等于和小于等于的情况。在图形中添加文本标签标明每条直线的方程和不等式类型，并在坐标系中用不同颜色填充表示解集的区域，最后在直线上标记系统解的位置。
以上提示语为根据原始绘图命令整理而来，仅供参考。