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Slope and Intercept of a Linear Function

Slope and Intercept of a Linear Function
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2025-12-17 21:50
In collections Lineare Funktionen
This example uses multiple-choice questions to help students understand the concepts of slope and intercept of a linear function. By analyzing the given linear function g(x) = 4x + 7.5, students can grasp the definitions of slope and intercept and their representations in the graph. GeoGebra commands such as Sequence, Element, Textfield, Join, etc., are used for constructing the graph. Suitable fo

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {7, 6, 7, 3, 1, 2, 7, 8, 4, 7}
  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. If(step ≟ 1, PosImgKind2 + (-1.5, 6.25), PosImgVali2 + (-0.35, 1.25)) → PosSB
  8. PolyLine(PosSB, Corner[txt011, 1] + (-0.1, 0.25), Corner[txt011, 1] + (-0.1, -0.1), Corner[txt011, 2] + (0.1, -0.1), Corner[txt011, 3] + (0.1, 0.1), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 1] + (-0.1, 0.75), PosSB) → sb01
  9. PolyLine(PosSB, Corner[txt031, 1] + (-0.1, 1.25), Corner[txt031, 1] + (-0.1, -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, 1.75), PosSB) → sb03
  10. 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
  11. 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
  12. 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
  13. PolyLine(PosSB, Corner[txt081, 1] + (-0.1, 0.25), Corner[txt081, 1] + (-0.1, -0.1), Corner[txt081, 2] + (0.1, -0.1), Corner[txt081, 3] + (0.1, 0.1), Corner[txt081, 4] + (-0.1, 0.1), Corner[txt081, 1] + (-0.1, 0.75), PosSB) → sb08
  14. PolyLine(PosSB, Corner[txt091, 1] + (0.25, -0.1), Corner[txt091, 2] + (0.1, -0.1), Corner[txt091, 3] + (0.1, 0.1), Corner[txt091, 4] + (-0.1, 0.1), Corner[txt091, 1] + (-0.1, 0.25), PosSB) → sb09
  15. PolyLine(PosSB, Corner[txt101, 1] + (0.25, -0.1), Corner[txt101, 2] + (0.1, -0.1), Corner[txt101, 3] + (0.1, 0.1), Corner[txt101, 4] + (-0.1, 0.1), Corner[txt101, 1] + (-0.1, 0.25), PosSB) → sb10
  16. PolyLine(PosSB, Corner[txt111, 1] + (0.25, -0.1), Corner[txt111, 2] + (0.1, -0.1), Corner[txt111, 3] + (0.1, 0.1), Corner[txt111, 4] + (-0.1, 0.1), Corner[txt111, 1] + (-0.1, 0.25), PosSB) → sb11
  17. Textfield(input021) → InputBox021
  18. Textfield(input051) → InputBox051
  19. SelectedIndex(dropdown041) → index041
  20. SelectedIndex(dropdown061) → index061
  21. SelectedIndex(dropdown091) → index091
  22. SelectedIndex(dropdown101) → index101
  23. SelectedIndex(dropdown111) → index111
  24. Segment(Origin + ((minX / stepX * disX) - edgeAxisX, 0), Origin + ((maxX / stepX * disX) + edgeAxisX, 0)) → segAxisX
  25. Segment(Origin + (0, (minY / stepY * disY) - edgeAxisY), Origin + (0, (maxY / stepY * disY) + edgeAxisY)) → segAxisY
  26. Sequence(Origin + ((minX / stepX * disX), 0) + (k * (disX, 0)), k, 0, maxX / stepX - minX / stepX) → PointsXAxis
  27. Sequence(Origin + (0, (minY / stepY * disY)) + (k * (0, disY)), k, 0, maxY / stepY - minY / stepY) → PointsYAxis
  28. Sequence(Segment[PointsXAxis(k) + (0, (-disSeg)), PointsXAxis(k) + (0, disSeg)], k, 1, Length[PointsXAxis]) → segXAxis
  29. Sequence(Segment[PointsYAxis(k) + ((-disSeg), 0), PointsYAxis(k) + (disSeg, 0)], k, 1, Length[PointsYAxis]) → segYAxis
  30. Sequence(m, m, minX, maxX, stepX) → numbersXAxis
  31. 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
  32. Sequence(m, m, minY, maxY, stepY) → numbersYAxis
  33. 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
  34. 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
  35. If(step ≤ 7, sliderK03, step ≟ 8, sliderK08, step ≟ 9, sliderK09, step ≟ 10, sliderK10, sliderK11) → valueK
  36. If(step ≥ 8, sliderD08, step ≟ 3, sliderD03, step ≟ 4, sliderD04, step ≟ 5, sliderD05, sliderD06) → valueD
  37. Segment(PAxisRO, PAxisRU) → segAxisR
  38. If(valueD > -1 ∨ step > 8, Intersect[FuncTransform, polyAxis], Intersect[FuncTransform, segAxisR]) → IP1
  39. Text("\textsf{\bold{f}}", IP1, false, true, 0, -1) → CapF
  40. Segment(Origin, Origin + (valueD * (0, disY))) → segD
  41. Text("\textsf{\bold{\textcolor{#DB6114}{d}}}", Midpoint[segD] + (-0.3, 0), false, true, -1, 0) → CapD
  42. Text("\footnotesize{\textsf{\bold{\textcolor{#988C00}{1}}}}", Midpoint[Origin + (0, (disY * valueD)), Origin + (disX, (disY * valueD))], false, true, 0, -1) → CapK1
  43. Text((("\footnotesize{\textsf{\bold{\textcolor{#988C00}{k = " * ReplaceAll[(("\(" * valueK) * "\)"), ".", ","]) * "}}}}"), Midpoint[Origin + (disX, (disX * valueK) + (disY * valueD)), Origin + (disX, (disY * valueD))], false, true, 1, 0) → CapK2
  44. If(step ≟ 2, correct021 ∧ correctdd021 ∧ correctdd022 ∧ correctdd023, step ≟ 7, correctdd071 ∧ correctdd072, step ≟ 8, moved08, step ≟ 9, correctdd091 ∧ moved09 ∧ valueKHelp > 0, step ≟ 10, correctdd101 ∧ moved10 ∧ valueKHelp < 0, step ≟ 11, correctdd111 ∧ moved11 ∧ valueKHelp ≟ 0, step ≟ 3, true, moved03, step ≟ 4, correctdd041 ∧ moved04 ∧ valueDHelp < 0, step ≟ 5, correct051 ∧ moved05 ∧ valueDHelp ≟ 0, step ≟ 6, correctdd061 ∧ moved06 ∧ valueDHelp > 0) → clickableBtnNext
  45. Segment(Origin071 + (fac07 * ((minX / stepX * disX) - edgeAxisX, 0)), Origin071 + (fac07 * ((maxX / stepX * disX) + edgeAxisX, 0))) → segAxisX071
  46. Translate(segAxisX071, Vector[Origin071, Origin072]) → segAxisX072
  47. Translate(segAxisX072, Vector[Origin071, Origin072]) → segAxisX073
  48. Segment(Origin071 + (fac07 * (0, (minY / stepY * disY) - edgeAxisY)), Origin071 + (fac07 * (0, (maxY / stepY * disY) + edgeAxisY))) → segAxisY071
  49. Translate(segAxisY071, Vector[Origin071, Origin072]) → segAxisY072
  50. Translate(segAxisY072, Vector[Origin071, Origin072]) → segAxisY073
  51. Sequence(Segment[Origin071 + (fac07 * ((minX * disX) + ((k - 1) * disX), 0)) + (fac07 * (0, (-disSeg))), Origin071 + (fac07 * ((minX * disX) + ((k - 1) * disX), 0)) + (fac07 * (0, disSeg))], k, 1, Length[PointsXAxis] - 1) → segXAxis071
  52. Translate(segXAxis071, Vector[Origin071, Origin072]) → segXAxis072
  53. Translate(segXAxis072, Vector[Origin071, Origin072]) → segXAxis073
  54. Sequence(Segment[Origin071 + (fac07 * (0, (minY * disX) + ((k - 1) * disY))) + (fac07 * ((-disSeg), 0)), Origin071 + (fac07 * (0, (minY * disX) + ((k - 1) * disY))) + (fac07 * (disSeg, 0))], k, 1, Length[PointsXAxis] - 1) → segYAxis071
  55. Translate(segYAxis071, Vector[Origin071, Origin072]) → segYAxis072
  56. Translate(segYAxis072, Vector[Origin071, Origin072]) → segYAxis073
  57. Segment(Origin071, Intersect[FuncTransform071(x), segAxisY071]) → segD071
  58. Segment(Origin072, Intersect[FuncTransform072(x), segAxisY072]) → segD072
  59. Segment(Origin + ((0 * disX), (2 * disY)), Origin + ((7 * disX), (2 * disY))) → segHelperParraO
  60. Segment(Origin + ((0 * disX), (0 * disY)), Origin + ((7 * disX), (0 * disY))) → segHelperParraU
  61. Segment(Origin073 + (fac07 * ((0 * disX), (2 * disY))), Origin073 + (fac07 * ((7 * disX), (2 * disY)))) → segHelperParra012O
  62. Segment(Origin073 + (fac07 * ((0 * disX), (0 * disY))), Origin073 + (fac07 * ((7 * disX), (0 * disY)))) → segHelperParra071U
  63. Text("\textsf{\bold{\scriptsize{\textcolor{98800C}{k = 0}}}}", Origin073 + (fac07 * ((7.2 * disX), (0.85 * disY))), false, true, 1, 1) → txt122
  64. Text("\textsf{\bold{\textcolor{50c1ce}{Zieh mich!}}}", PosSlider + If[step ≟ 6, (-0.35, 0.25), (2.2, 0.25)], false, true, 1, 1) → CapZiehMichD
  65. Text("\textsf{\bold{\textcolor{50c1ce}{Zieh mich!}}}", PosSlider + If[step ≟ 9, (0.9, 0.25), (2.2, 0.25)], false, true, 1, 1) → CapZiehMichK