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Graphing a Homogeneous Linear Function

Graphing a Homogeneous Linear Function
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2025-10-04 19:01
In collections Homogen lineare Funktionen
This example demonstrates how to graph a homogeneous linear function. Key mathematical concepts include the slope and graph of a linear function. GeoGebra commands used include Sequence, Element, Textfield, Join, etc. Suitable for 7-8th grade students.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {4, 5, 1, 4, 7, 10, 7, 4, 1, 9}
  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 ≟ 3, OriginalOrigin + (0, (3 * disY / stepY)), OriginalOrigin) → Origin
  8. If(step ≟ 3, -4, -1) → minY
  9. If(step ≟ 3, 3, 6) → maxY
  10. Segment(Origin + ((minX / stepX * disX) - edgeAxisX, 0), Origin + ((maxX / stepX * disX) + edgeAxisX, 0)) → segAxisX
  11. Segment(Origin + (0, (minY / stepY * disY) - edgeAxisY), Origin + (0, (maxY / stepY * disY) + edgeAxisY)) → segAxisY
  12. Sequence(Origin + ((minX / stepX * disX), 0) + (k * (disX, 0)), k, 0, maxX / stepX - minX / stepX) → PointsXAxis
  13. Sequence(Origin + (0, (minY / stepY * disY)) + (k * (0, disY)), k, 0, maxY / stepY - minY / stepY) → PointsYAxis
  14. Sequence(Segment[PointsXAxis(k) + (0, (-disSeg)), PointsXAxis(k) + (0, disSeg)], k, 1, Length[PointsXAxis]) → segXAxis
  15. Sequence(Segment[PointsYAxis(k) + ((-disSeg), 0), PointsYAxis(k) + (disSeg, 0)], k, 1, Length[PointsYAxis]) → segYAxis
  16. Sequence(m, m, minX, maxX, stepX) → numbersXAxis
  17. 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
  18. Sequence(m, m, minY, maxY, stepY) → numbersYAxis
  19. 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
  20. 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
  21. Segment(Origin + (-0.2, 0.2), Origin + (-0.75, 0.75)) → segUrsprung
  22. Element({4, 1, 3}, step) → denSteigung
  23. Segment(Origin, Origin + ((denSteigung * disX / stepX), 0)) → seg11
  24. Element({3, 2, -2}, step) → numSteigung
  25. Segment(Point[seg11, 1], Point[seg11, 1] + (0, (numSteigung * disY / stepY))) → seg12
  26. Point(seg12, 1) → PosP
  27. Text("\textsf{\bold{\textcolor{616161}{P}}}", PosP + (0.05, 0.1), false, true, 1, 0) → CapPosP
  28. Segment(Origin, Point[seg12, 1]) → seg13
  29. Intersect(FuncTransform, polyAxis) → PosIntersect_{1}, PosIntersect_{2}
  30. Text("\textsf{\bold{f}}", PosIntersect_{2} + (-0.25, 0.25), false, true, 0, 0) → CapF
  31. Text((("\textsf{\bold{{" * denSteigung) * "}}}"), Midpoint[seg11], false, true, 0, 1) → CapSeg11
  32. Text("\textsf{\footnotesize{Ursprung\\(0|0)}}", Point[segUrsprung, 1] + (0.2, 0.2), false, true, -1, 0) → CapUrsprung
  33. Text((("\textsf{\bold{{\(" * numSteigung) * "\)}}}"), Midpoint[seg12], false, true, 1, 0) → CapSeg12