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Constructing One-Variable Equations

Constructing One-Variable Equations
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2023-01-02 19:32
FunctionCoordinate Geometry
This example demonstrates how to construct one-variable equations with 0, 1, or infinite solutions by adjusting the slope and intercept of lines. Key math concepts include the solutions of linear equations. GeoGebra commands used include Shuffle, Element, Polynomial, etc. Suitable for 6-8 grade students.

GeoGebra Commands & Parameters

  1. Shuffle(Flatten[{Sequence[3], Sequence[3], Sequence[3]}]) → randomList2, {2, 2, 1, 1, 1, 3, 2, 3, 3}
  2. Shuffle(Flatten[{Sequence[4], Sequence[4], Sequence[4]}]) → randomList1, {2, 3, 4, 1, 2, 3, 1, 4, 4, 1, 2, 3}
  3. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  4. Polynomial((a * x) + b) → left
  5. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  6. Polynomial(Element[{g1, g2, g3, g4}, randomNum1]) → right
  7. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  8. Corner(5) → layoutAppSize
  9. RemoveUndefined({a, b, c, d, f, g}) → inputCurrent
  10. Textfield(a) → InputBox1
  11. Textfield(b) → InputBox2
  12. Textfield(c) → InputBox3
  13. Textfield(d) → InputBox4
  14. Textfield(f) → InputBox5
  15. Corner(5) → AppSize
  16. If(randomNum1 ≠ 4, 352, 320) → PosXIB4
  17. If(randomNum1 ≠ 4, 420, 495) → PosXText4
  18. Textfield(g) → InputBox6
  19. Translate(hguideline, Vector[(Vector[Corner[4], Corner[1]] / 500 * 24)]) → hguideline24
  20. Polynomial((If[randomNum2 ≟ 1, aAlt, a] * x) + If[randomNum2 ≟ 2, bAlt, b]) → rightSol

AI Drawing Prompt Reference

Draw a coordinate plane with randomly generated lines, adjusting their slopes and intercepts to show equations with 0, 1, or infinite solutions. Include randomly selected numbers and polynomials, with different colors for the left and right sides of the equations, and text boxes to display parameter values. Start by drawing the lines, then mark the random numbers and polynomials, and finally adjust their positions and sizes to fit the interface.
The prompt above was compiled from the original drawing commands and is for reference only.