Tables, Graphs, and Linear Equations

Tables, Graphs, and Linear Equations
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2023-01-20 00:27
This example explores the relationship between tables, graphs, and algebraic equations to help students understand the graphing of linear functions. It involves using ordered pairs from tables to draw linear function graphs, with commands like Shuffle, Element, Zip, Sequence, Sort, Point, and TableText. Suitable for 6-8th grade students.

GeoGebra Commands & Parameters

  1. Shuffle({1, 2, 3, 4}) → goodPtsPos, {4, 3, 1, 2}
  2. Shuffle({-1, 1, -2, 2}) → mList, {-1, 1, -2, 2}
  3. Shuffle(Sequence[t, t, -4, 3] \ {0}) → bList, {-4, -3, -1, 3, 1, -2, 2}
  4. Element(mList, Mod[mbCount, Length[mList]] + 1) → m
  5. Element(bList, Mod[mbCount, Length[bList]] + 1) → b
  6. Zip((xList(n), yList(n)), n, goodPtsPos) → goodPts
  7. Sequence((bad1XList(n), r1Bad(bad1XList(n))), n, 1, Length[bad1XList]) → bad1Pts
  8. Sequence((bad2XList(n), r2Bad(bad2XList(n))), n, 1, Length[bad2XList]) → bad2Pts
  9. Sort(allPoints) → sortedPts
  10. Corner(5) → AppSize
  11. Polygon((-7.7, -8.9), (7.7, -8.9), (7.7, 8.9), (-7.7, 8.9)) → peep, f, g, h, i
  12. Segment((-7.69, 0), (7.69, 0)) → axisX
  13. Segment((0, -8.95), (0, 8.95)) → axisY
  14. If(firstCol ∧ x(LastClicked) ≟ -2, yRef, secondCol ∧ x(LastClicked) ≟ -1, yRef + 52, thirdCol ∧ x(LastClicked) ≟ 0, yRef + (2 * 52), fourthCol ∧ x(LastClicked) ≟ 2, yRef + (3 * 52), 151) → yPosSubst
  15. Element(allPulsingPoints, pulsingIndexList(pulsingIndex)) → pulsingPoint
  16. circlePixels(pulsingPoint, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject
  17. Sum({clickedP1, clickedP2, clickedP3}) → countClicked
  18. Point({-25.7, -8.2}) → T1
  19. Polygon({T1, T2, T3, T4}) → fullTable
  20. Segment(V11, V41) → vertCol1
  21. Segment(V12, V42) → vertCol2
  22. Segment(H4, H3) → headLine
  23. Segment(L11, L12) → horLine1
  24. Segment(L21, L22) → horLine2
  25. Segment(L31, L32) → horLine3
  26. Polygon({L11, L12, H3, H4}) → box1
  27. Polygon({L21, L22, L12, L11}) → box2
  28. Polygon({L31, L32, L22, L21}) → box3
  29. Polygon({T1, T2, L32, L31}) → box4
  30. Zip(IndexOf[A, allPoints], A, sortedPts) → tabValues
  31. Sequence(((((((("\bold{" * yList(A)) * "}=") * m) * "\cdot\bold{(") * xList(A)) * ")}") * If[b ≟ 0, "", b > 0, ("+" * b), ("-" * abs(b))]), A, 1, 4) → textVerifyAll
  32. Sequence(("" * If[Defined[IndexOf[sortedPts(A), goodPts]], (((((("Plugging \(" * sortedPts(A)) * "\) into the equation of line \(") * r) * " \), we get \(") * textVerifyAll(goodPtsPos(IndexOf[sortedPts(A), goodPts]))) * " \)"), (((("The point \(" * sortedPts(A)) * "\) does not belong to line \(") * r) * "\). ")]), A, 1, 13) → altTabPoints
  33. Sequence(false, A, 1, 13) → allFalse
  34. Sequence((((("SetFixed(Tab" * A) * ",true,!pointsClicked(") * A) * "))"), A, 1, 13) → cmdLock
  35. Append("\bold{\(x\)}", Zip[(("\mathsf{" * A) * "}"), A, xList]) → col1
  36. Append("\bold{\(y\)}", Zip[(("\mathsf{" * A) * "}"), A, yList]) → col2
  37. Zip(pointsClicked(IndexOf[(A, B), sortedPts]), A, xList, B, yList) → clickedRows
  38. Append((("\bold{\(" * textLine) * "\)}"), Zip[(("\math{" * If[clickedRows(A), B, "\hspace{200px}"]) * "}"), A, {1, 2, 3, 4}, B, {textVerifyLine1, textVerifyLine2, textVerifyLine3, textVerifyLine4}]) → col3
  39. TableText(col1, col2, col3, "vc", 75, 50) → data
  40. Sequence({(("SetColor(Tab" * A) * ", colorCorrect)"), (("SetValue(pointsClicked," * A) * ",true)"), (("SetValue(LastClicked," * sortedPts(A)) * ")")}, A, 1, 13) → cmdCorrect
  41. Sequence({(("SetColor(Tab" * A) * ", colorWrong)"), (("SetPointStyle(Tab" * A) * ",1)"), (("SetValue(pointsClicked," * A) * ",true)"), "SetValue(LastClicked,(?,?))"}, A, 1, 13) → cmdWrong
  42. Sequence(Defined[IndexOf[sortedPts(A), goodPts]], A, 1, 13) → isSolutionPt
  43. IndexOf((xList(1), yList(1)), sortedPts) → indexRow1
  44. IndexOf((xList(2), yList(2)), sortedPts) → indexRow2
  45. IndexOf((xList(3), yList(3)), sortedPts) → indexRow3
  46. IndexOf((xList(4), yList(4)), sortedPts) → indexRow4
  47. Polygon({T1, T2, T3, T4}) → box0
  48. Point({-35, -5}) → T0

AI Drawing Prompt Reference

This is a graphic showing a linear function, a table, and coordinate axes. It includes axes, a linear function graph made of points from a table, a table of x and y values, and a point array. The linear function graph is drawn from ordered pairs in the table, and the axes provide reference for the points. The table displays the values, and the point array marks key points. The overall layout is: first draw the axes, then the linear function graph, then the table and point array, and finally enclose the points and table in a rectangular frame.
The prompt above was compiled from the original drawing commands and is for reference only.