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Writing Equations of Proportional Relationships

Writing Equations of Proportional Relationships
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2022-03-26 02:39
FunctionCoordinate GeometrySlider AnimationGraphing
This example demonstrates how to write equations of proportional relationships through graphical methods. It involves core math concepts like proportional relationships, linear equations, function graphs, ratios, and coordinate geometry. GeoGebra commands and objects used include PointIn, Random, Dilate, Vector, Segment, If, and Textfield. Suitable for middle school and above students to understand the method of writing equations for proportional relationships.

GeoGebra Commands & Parameters

  1. PointIn(g_1) → D
  2. Random(1, 15) → y_1, 13
  3. Random(1, 15) → x_1, 12
  4. Random(20, 75) → k, 48
  5. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], A) → B'
  6. Vector(B, B') → u
  7. Dilate(A, If[2 < a ≤ 3, 3 - a, 0], (0, y(D))) → A'
  8. Vector(A, A') → v
  9. Dilate(A', If[3 < a ≤ 4, 4 - a, 0], D) → C'
  10. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], (x(D), y(D) + y(A'))) → D'
  11. Vector(D, D') → c
  12. Dilate(D', If[6 < a ≤ 7, 7 - a, 0], (x(D') + x(D), y(D'))) → E'
  13. Dilate(A, If[8 < a ≤ 9, 9 - a, 0], D) → A'_{1}
  14. Segment(A, A'_{1}) → g
  15. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E) → D'_{1}
  16. Random(-10, 10) → b_1, -5
  17. Random(-10, 10) → n_1, -3
  18. Random(1, 10) → d_1, 5
  19. If(s ≥ 0, "earn", "lose") → text7
  20. If(d > 1, "hours", "hour") → text8
  21. Textfield(p) → InputBox3
  22. Textfield(o) → InputBox1
  23. If(o ≟ n_1 / d_1, "Yes!", "no") → text9
  24. If(p ≟ q, "Yes!", "no") → text10
  25. Vector(A', C') → w
  26. Vector(D', E') → e
  27. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E') → D'_{2}
  28. Segment(D, D'_{2}) → h
  29. Textfield(q_1) → InputBox2
  30. If(q ≟ q_1, "Nice job!", "No. Try again.") → text17

AI Drawing Prompt Reference

Draw a graph of a proportional relationship by generating a series of points and segments through proportional transformations. Start by randomly selecting point D on a line, then generate points B', A', C', D', and E' using proportional transformations, and connect these points with segments. Next, use random numbers to generate a slope and y-intercept, draw the line y = kx + b, and use input boxes to input point coordinates and verify if the points lie on the line.
The prompt above was compiled from the original drawing commands and is for reference only.