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Linear Growth Modeling & Solving Linear Systems by Graphing

Linear Growth Modeling & Solving Linear Systems by Graphing
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2019-07-16 01:25
FunctionCoordinate GeometryGraphing
This example demonstrates dynamic illustration of linear growth models, visually showcasing the process of solving linear systems of equations through graphs. Core math concepts include linear functions, straight lines, function graphs, linear systems, and intersection solving. Construction highlights GeoGebra commands/objects like Textfield, Intersect, Dilate, Segment from the summary. Suitable for high school mathematics education to understand the correlation between linear function graphs and system solving, and the application of dynamic geometric transformations.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox9
  2. Textfield(g) → InputBox10
  3. Textfield(h) → InputBox11
  4. Textfield(k) → InputBox7
  5. Textfield(e) → InputBox1
  6. Textfield(i) → InputBox2
  7. Textfield(j) → InputBox3
  8. Textfield(l) → InputBox4
  9. Textfield(r) → InputBox5
  10. Textfield(s) → InputBox6
  11. Textfield(t) → InputBox8
  12. Textfield(u) → InputBox12
  13. Intersect(f_1, f_2, 1) → C
  14. Intersect(f_1, g_1, 1) → D
  15. Intersect(f_2, g_1, 1) → E
  16. Dilate(B, If[2 < v ≤ 3, 3 - v, 0], C) → B'
  17. Dilate(C, If[2 < v ≤ 4, 4 - v, 0], E) → C'
  18. Dilate(A, If[0 < v ≤ 1, 1 - v, 0], C) → A'
  19. Segment(A, A') → i_1
  20. Dilate(C, If[1 < v ≤ 2, 2 - v, 0], D) → C'_1
  21. Segment(C, C'_1) → j_1
  22. Segment(B, B') → h_1
  23. Segment(C, C') → k_1

AI Drawing Prompt Reference

Draw two lines f and g defined by user-input functions f(x) and g(x). Find their intersection points C and D. Use the Dilate command to scale point B to B' with C as the center, and scale point C to C' with E as the center. Then, scale point A to A' with C as the center and connect A and A' to form line segment i. Similarly, scale point C to C'_1 with C as the center, scale point C to C' with D as the center, and connect C and C'_1 to form line segment j. Connect B and B' to form line segment h, and connect C and C' to form line segment k.
The prompt above was compiled from the original drawing commands and is for reference only.