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Evaluating Unknowns in Linear Equations in Two Variables and Graphing the Equati

Evaluating Unknowns in Linear Equations in Two Variables and Graphing the Equati
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2016-06-06 02:21
FunctionSequenceCoordinate GeometrySlider AnimationGraphing
① This interactive GeoGebra activity demonstrates how to solve for unknowns in linear equations with two variables and simultaneously graphs the corresponding lines, helping students visualize the connection between algebraic solutions and geometric representations. ② Core mathematical concepts include linear equations in two variables, linear functions, slope and intercept, graphing lines on the coordinate plane, and solving for unknowns via substitution or elimination. ③ Construction highlights: The activity uses an InputBox for user answers, with commands such as TextToUnicode, Length, If, Sum, RandomElement, Simplify, Sequence, Sort, Join, Remove, Insert, Element, GCD, TableText, Textfield, CoordPointertoAxes6, IndexOf, Point, Vector, Min, and Max to parse input, generate random problems, create tables, and plot points and lines. ④ Suitable for middle school to high school students as an individual lesson review or classroom practice, and for teachers to demonstrate the integration of solving and graphing linear equations.

GeoGebra Commands & Parameters

  1. TextToUnicode(usertxtanswerq) → listdigitsq
  2. Length(listdigitsq) → lengthlistdigitsq
  3. If(Element[listdigitsq, 1] ≟ 45, 2, 1) → startindexq
  4. Sum((If[Element[listdigitsq, 1] ≟ 45, -1, 1] * Sequence[((Element[listdigitsq, i] - 48) * 10^(lengthlistdigitsq - i)), i, startindexq, lengthlistdigitsq])) → useranswerqnum
  5. TextToUnicode(usertxtanswerp) → listdigitsp
  6. If(Element[listdigitsp, 1] ≟ 45, 2, 1) → startindexp
  7. Length(listdigitsp) → lengthlistdigitsp
  8. Sum((If[Element[listdigitsp, 1] ≟ 45, -1, 1] * Sequence[((Element[listdigitsp, i] - 48) * 10^(lengthlistdigitsp - i)), i, startindexp, lengthlistdigitsp])) → useranswerpnum
  9. RandomElement({-1, 1, 2, -2, -3, 3, 4, -4, -1, 1, -2, 2, 5, -5, -1, 1}) → a_1
  10. RandomElement({0, -1, 1, 2, -2, -3, 3, 0, -1, 1, -2, 2, 4, -4, 0, -1, 1, -2, 2, 5, -5, 0, -1, 1, -2, 2}) → n_3
  11. RandomElement({-1, 0, 1, 2, -2, 0, -3, 3}) → x_g
  12. RandomElement({-1, 1, 2, -2, -3, 3, 4, -4, -1, 1, -2, 2, 5, -5, -1, 1}) → b_1
  13. Simplify(If[-10 ≤ x ≤ 10, ((-(x(e_n) / y(e_n))) * x) - z(e_n) / y(e_n)]) → f
  14. Sequence(abs(f(0) - (a_1 / b_1 * i) - round(f(0) - (a_1 / b_1 * i), 0)), i, 0, abs(b_1 - 1)) → listsearch1stinteger, {0, 0, 0}
  15. Sort(Sequence[xInty + (b_1 * i), i, -2, 2, 1]) → listxno
  16. RandomElement({1, 2, 3, 4}) → shiftposty
  17. Join({{x}, listxno}) → listx
  18. RandomElement(Remove[{1, 2, 3, 4}, {shiftposty}]) → shiftpostx
  19. Remove(listx, {Element[listx, shiftpostx + 1]}) → listprex
  20. Join({{y}, (m * listxno) + d}) → listy
  21. Remove(listy, {Element[listy, shiftposty + 1]}) → listprey
  22. Insert("p", listprey, shiftposty + 1) → listypost
  23. Element(listy, shiftposty + 1) → answerp
  24. Element(listx, shiftposty + 1) → x_p
  25. GCD({a_1, b_1, c_1}) → c_g
  26. Insert("q", listprex, shiftpostx + 1) → listxpost
  27. TableText({listxpost, listypost}, "c_|h") → txtTableValues
  28. Element(listy, shiftpostx + 1) → y_q
  29. Textfield(usertxtanswerp) → InputBox1
  30. Textfield(usertxtanswerq) → InputBox2
  31. If(useranswerpnum ≟ Element[listy, shiftposty + 1], true, false) → answerpcorrect
  32. If(useranswerqnum ≟ Element[listx, shiftpostx + 1], true, false) → answerqcorrect
  33. Element(listx, shiftpostx + 1) → answerq
  34. CoordPointertoAxes6(P) → A, B, text2, text3, text4, text5, text6, u, v
  35. CoordPointertoAxes6(Q) → C, D, text7, text8, text9, text10, text11, w, a
  36. IndexOf("p", listypost) → indexofp
  37. IndexOf("q", listxpost) → indexofq
  38. Sequence((Element[listxno, i], Element[listyno, i]), i, 1, 5) → listallpoints
  39. Point(Circle[P_{useranswerq}, x(P_{useranswerq})]) → E_o
  40. Vector(P_{useranswerq}, (x(P_{useranswerq}), 0)) → g
  41. Vector(P_{useranswerp}, (0, y(P_{useranswerp}))) → b
  42. Min(Min[listxno] - ((Max[listxno] - Min[listxno]) * 0.2), Min[-2, If[Defined[useranswerqnum], useranswerqnum - 1, 0]]) → xMin
  43. Max(Max[listxno] + ((Max[listxno] - Min[listxno]) * 0.1), Max[2, If[Defined[useranswerqnum], useranswerqnum - 1, 0]]) → xMax
  44. Max(Max[listyno] + ((Max[listyno] - Min[listyno]) * 0.1), Max[2, If[Defined[useranswerpnum], useranswerpnum + 1, 0]]) → yMax
  45. Min(Min[listyno] - ((Max[listyno] - Min[listyno]) * 0.1), Min[-2, If[Defined[useranswerpnum], useranswerpnum - 1, 0]]) → yMin
  46. Point(e_n) → E
  47. Vector(E, (x(E), 0)) → c
  48. Vector(E, (0, y(E))) → e