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Concept of Gradient (Slope) of a Line

Concept of Gradient (Slope) of a Line
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2018-01-01 09:33
AngleFunctionCoordinate GeometrySlider AnimationGraphing
In collections Mathematics Form 2
This interactive GeoGebra example visually demonstrates the geometric meaning of the gradient (slope) of a straight line. The core mathematical concept is the definition of slope as the ratio of vertical change to horizontal change between two points on a line, along with how positive and negative slopes indicate the direction of inclination. Construction highlights: the Line command draws the line, Slope command computes and displays the slope value, Intersect finds intercepts with axes, Segment and Length build a right triangle for visual ratio, Midpoint marks midpoints, Circle and Angle illustrate related angle relationships, and Text adds dynamic labels. Suitable for middle school to high school students learning linear functions, coordinate geometry, or introductory calculus, this example helps learners intuitively grasp the connection between slope, angle of inclination, sign, and rate of change.

GeoGebra Commands & Parameters

  1. SelectedIndex(Bahasa) → nn
  2. If(nn ≟ 1, LaTeX["\text{Undefined}"], LaTeX["\text{Tidak tertakrif}"]) → Tex5
  3. Line(P, Q) → f
  4. Slope(f) → s
  5. If(y(P) < y(Q), P, Q) → M
  6. If(y(P) < y(Q), Q, P) → N
  7. Line(M, xAxis) → g
  8. Line(N, yAxis) → h
  9. Intersect(g, h) → A
  10. Segment(M, A) → i
  11. Segment(N, A) → j
  12. Length(i) → b
  13. Length(j) → c
  14. Midpoint(i) → B
  15. Midpoint(j) → C
  16. Circle(C, 0.8) → d
  17. Line(C, xAxis) → k
  18. Intersect(d, k) → D, E
  19. If(nn ≟ 1, " units", " unit") → UTex
  20. If(b ≤ 1, Text[b] + " unit", Text[b] + UTex) → Tex1
  21. If(c ≤ 1, Text[c] + " unit", Text[c] + UTex) → Tex2
  22. If(c ≤ 1, Text[c] + " unit", Text[c] + UTex) → Tex3
  23. If(y(Q) < 0, "(" + (Text[y(Q)]) + ")", Text[y(Q)]) → TyQ
  24. Text(x(P)) → TxP
  25. If(x(Q) < 0, "(" + (Text[x(Q)]) + ")", Text[x(Q)]) → TxQ
  26. Text(y(P)) → TyP
  27. If(Defined[s] ≟ false, Tex5, If[s ≥ 0, FractionText[(y(P) - y(Q)) / (x(P) - x(Q))], LaTeX["-" + (FractionText[(y(Q) - y(P)) / (x(P) - x(Q))])]]) → Gft
  28. If(a ≟ true, Gft, Text[(y(P) - y(Q)) / (x(P) - x(Q))]) → Gt
  29. Angle(M, A, N) → α
  30. If(nn ≟ 1, LaTeX["\text{Gradient of line PQ"], LaTeX["\text{Kecerunan garis PQ}"]) → text1
  31. If(nn ≟ 1, "Line that slopes up", "Garis condong ke atas") → KecPos
  32. If(nn ≟ 1, "Line that slopes down", "Garis condong ke bawah") → KecNeg
  33. If(nn ≟ 1, "Horizontal line", "Garis mengufuk") → KecSifar
  34. If(nn ≟ 1, "Vertical line", "Garis menegak") → Kectt
  35. If(s > 0, KecPos, s < 0, KecNeg, s ≟ 0, KecSifar, Defined[s] ≟ false, Kectt) → Tex4