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寻找通过两个给定点的函数方程

寻找通过两个给定点的函数方程
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2025-12-17 22:05
所属专题 Lineare Funktionen
本范例演示如何通过两个已知点确定线性函数的方程。核心数学概念包括斜率计算、截距确定及函数图像绘制。作图要点涉及使用GeoGebra命令如Sequence、Point、Segment和Intersect来构造点、绘制线段及计算交点。适合中学数学教学，尤其适用于七至八年级学生掌握函数与图像关系。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 2, 9, 6, 5, 3, 4, 5, 9, 2}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  7. PolyLine(PosSB, Corner[txt031, 1] + (0.25, -0.1), Corner[txt031, 2] + (0.1, -0.1), Corner[txt031, 3] + (0.1, 0.1), Corner[txt031, 4] + (-0.1, 0.1), Corner[txt031, 1] + (-0.1, 0.25), PosSB) → sb03
  8. PolyLine(PosSB, Corner[txt041, 1] + (0.25, -0.1), Corner[txt041, 2] + (0.1, -0.1), Corner[txt041, 3] + (0.1, 0.1), Corner[txt041, 4] + (-0.1, 0.1), Corner[txt041, 1] + (-0.1, 0.25), PosSB) → sb04
  9. PolyLine(PosSB, Corner[txt051, 1] + (0.25, -0.1), Corner[txt051, 2] + (0.1, -0.1), Corner[txt051, 3] + (0.1, 0.1), Corner[txt051, 4] + (-0.1, 0.1), Corner[txt051, 1] + (-0.1, 0.25), PosSB) → sb05
  10. PolyLine(PosSB, Corner[txt061, 1] + (0.25, -0.1), Corner[txt061, 2] + (0.1, -0.1), Corner[txt061, 3] + (0.1, 0.1), Corner[txt061, 4] + (-0.1, 0.1), Corner[txt061, 1] + (-0.1, 0.25), PosSB) → sb06
  11. Segment(Origin + ((minX / stepX * disX) - edgeAxisX, 0), Origin + ((maxX / stepX * disX) + edgeAxisX, 0)) → segAxisX
  12. Segment(Origin + (0, (minY / stepY * disY) - edgeAxisY), Origin + (0, (maxY / stepY * disY) + edgeAxisY)) → segAxisY
  13. Sequence(Origin + ((minX / stepX * disX), 0) + (k * (disX, 0)), k, 0, maxX / stepX - minX / stepX) → PointsXAxis
  14. Sequence(Origin + (0, (minY / stepY * disY)) + (k * (0, disY)), k, 0, maxY / stepY - minY / stepY) → PointsYAxis
  15. Sequence(Segment[PointsXAxis(k) + (0, (-disSeg)), PointsXAxis(k) + (0, disSeg)], k, 1, Length[PointsXAxis]) → segXAxis
  16. Sequence(Segment[PointsYAxis(k) + ((-disSeg), 0), PointsYAxis(k) + (disSeg, 0)], k, 1, Length[PointsYAxis]) → segYAxis
  17. Sequence(m, m, minX, maxX, stepX) → numbersXAxis
  18. Sequence(Text[((("\textsf{\footnotesize{\(" * If[numbersXAxis(k) ≥ 0, "\phantom{\(-\)}", ""]) * If[Element[numbersXAxis, k] ≟ 0, "", ("" * Element[numbersXAxis, k])]) * "\)}}"), PointsXAxis(k) + (-0.12, (-disSeg)), false, true, 0, -1], k, 1, (maxX - minX) / stepX + 1) → CapX
  19. Sequence(m, m, minY, maxY, stepY) → numbersYAxis
  20. Sequence(Text[((("\textsf{\footnotesize{\(" * If[numbersYAxis(k) ≥ 0, "\phantom{\(-\)}", ""]) * If[Element[numbersYAxis, k] ≟ 0, "", ("" * Element[numbersYAxis, k])]) * "\)}}"), PointsYAxis(k) + ((-disSeg) + 0.05, 0), false, true, -1, 0], k, 1, (maxY - minY) / stepY + 1) → CapY
  21. Element({Polygon[(x(PointsXAxis(1)), y(PointsYAxis(1))) + ((-edgeAxisX) - 0.05, (-edgeAxisY) - 0.05), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(1))) + (edgeAxisX + 0.05, (-edgeAxisY) - 0.05), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(Length[PointsYAxis]))) + (edgeAxisX + 0.05, edgeAxisY + 0.05), (x(PointsXAxis(1)), y(PointsYAxis(Length[PointsYAxis]))) + ((-edgeAxisX) - 0.05, edgeAxisY + 0.05)]}, 1) → polyAxis
  22. Sequence(Sequence[(x(PointsXAxis(k)), y(PointsYAxis(m))), k, 1, Length[PointsXAxis]], m, 1, Length[PointsYAxis]) → AllPointsOnGrid
  23. PolyLine(PosSB, Corner[txt011, 1] + (-0.1, 0.25), Corner[txt011, 1] + (-0.1, 0), Corner[txt011, 2] + (0.1, 0), Corner[txt011, 3] + (0.1, 0.1), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 1] + (-0.1, 0.75), PosSB) → sb01
  24. Point(Join[{{ParkPoints02(1)}, AllPointsOnGrid}]) → Point022
  25. Point(Join[{{ParkPoints02(2)}, AllPointsOnGrid}]) → Point021
  26. Text("\textsf{\bold{\textcolor{#50c1ce}{Zieh mich!}}}", Midpoint[ParkPoints02(1), ParkPoints02(2)] + (0, 0.25), false, true, 0, 1) → CapZiehMich02
  27. Circle(Point021, radFB02) → circleFB021
  28. Circle(Point022, radFB02) → circleFB022
  29. Segment(Point031, Point031 + (Min[anim04, 1] * ((2 * disX), 0))) → segSD041
  30. Segment(Point031 + ((2 * disX), 0), Point031 + ((2 * disX), 0) + (Min[anim04 - 1, 1] * (0, (-4 * disY)))) → segSD042
  31. Segment(Point032, Point032 + ((anim04 - 2) * (Point031 - Point032))) → segFunc
  32. Text("\textsf{\bold{f}}", AllPointsOnGrid(10, 2), false, true, -1, 0) → CapF
  33. Textfield(input031) → InputBox031
  34. Textfield(input032) → InputBox032
  35. Textfield(input051) → InputBox051
  36. Textfield(input061) → InputBox061
  37. If(step ≟ 2, correct02 ∧ anim02 ≥ 1, true, step ≟ 3, correct031 ∧ correct032 ∧ correct033, step ≟ 4, anim04 ≟ 2, step ≟ 5, correct051 ∧ correct061, step ≟ 6, true) → clickableBtnNext
  38. Element({Polygon[(x(PointsXAxis(1)), y(PointsYAxis(1))) + ((-edgeAxisX) - 0.2, (-edgeAxisY) - 0.2), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(1))) + (edgeAxisX + 0.2, (-edgeAxisY) - 0.2), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(Length[PointsYAxis]))) + (edgeAxisX + 0.2, edgeAxisY + 0.2), (x(PointsXAxis(1)), y(PointsYAxis(Length[PointsYAxis]))) + ((-edgeAxisX) - 0.2, edgeAxisY + 0.2)]}, 1) → polyAxisStart
  39. PolyLine(PosSB, Corner[txt021, 1] + (0.25, -0.1), Corner[txt021, 2] + (0.1, -0.1), Corner[txt021, 3] + (0.1, 0.1), Corner[txt021, 4] + (-0.1, 0.1), Corner[txt021, 1] + (-0.1, 0.25), PosSB) → sb02
  40. Segment(Origin, Point031) → segd
  41. Text("\textsf{\textcolor{#1565c0}{\bold{d}}}", Midpoint[Origin, Point031] + ((-disX), 0), false, true, 0, 0) → Capd
  42. Intersect(FuncTransform, polyAxis) → PointFuncTransform02, PointFuncTransform01
  43. Segment(PointFuncTransform01, PointFuncTransform01 + (anim02 * (PointFuncTransform02 - PointFuncTransform01))) → segFunkDraw
  44. If(step ≟ 2, anim02 ≟ 0 ∨ anim02 ≟ 1, If[step ≟ 4, anim04 ≟ 0 ∨ anim04 ≟ 2, true]) → clickableBtnBack
  45. Text("\textsf{\bold{\footnotesize{\textcolor{#9c4381}{2}}}}", Midpoint[segSD041], false, true, 0, 1) → CapSD041
  46. Text("\textsf{\bold{\footnotesize{\textcolor{#db6114}{\(-\)4}}}}", Midpoint[segSD042] - (0, 0.2), false, true, 1, 0) → CapSD042