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Graphing a Line with Table of Values

Graphing a Line with Table of Values
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2020-11-21 20:30
FunctionCoordinate GeometryGraphing
This example demonstrates how to graph a line using a table of values. Key mathematical concepts include the equation of a line in coordinate geometry. Using GeoGebra commands such as Sequence, Point, and Vector, the construction of the line and its geometric interpretation are explored. Suitable for students in middle school and above learning about linear equations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon((1.3, 0), (2.2, 0), 4) → poly2
  2. Polygon((1.3, 1), (2.2, 1), 4) → poly5
  3. Polygon((0, 0), (0.9, 0), 4) → poly1
  4. Polygon((0, 1), (0.9, 1), 4) → poly4
  5. Polygon((1.3, 2), (2.2, 2), 4) → poly8
  6. Polygon((0, 2), (0.9, 2), 4) → poly7
  7. Segment(J, K) → a
  8. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → y1
  9. If(IsInRegion[A, poly7], 1, If[IsInRegion[B, poly7], 2, If[IsInRegion[C, poly7], 3, If[IsInRegion[D, poly7], 4, If[IsInRegion[E, poly7], 5, If[IsInRegion[F, poly7], 6, If[IsInRegion[G, poly7], 7, If[IsInRegion[H, poly7], 8, If[IsInRegion[I, poly7], 9, 0]]]]]]]]) → x1
  10. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → y2
  11. If(IsInRegion[A, poly4], 1, If[IsInRegion[B, poly4], 2, If[IsInRegion[C, poly4], 3, If[IsInRegion[D, poly4], 4, If[IsInRegion[E, poly4], 5, If[IsInRegion[F, poly4], 6, If[IsInRegion[G, poly4], 7, If[IsInRegion[H, poly4], 8, If[IsInRegion[I, poly4], 9, 0]]]]]]]]) → x2
  12. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → y3
  13. If(IsInRegion[A, poly1], 1, If[IsInRegion[B, poly1], 2, If[IsInRegion[C, poly1], 3, If[IsInRegion[D, poly1], 4, If[IsInRegion[E, poly1], 5, If[IsInRegion[F, poly1], 6, If[IsInRegion[G, poly1], 7, If[IsInRegion[H, poly1], 8, If[IsInRegion[I, poly1], 9, 0]]]]]]]]) → x3
  14. Sequence(Point[{i + 0.1, 6}], i, -3, 5) → anchors
  15. Segment((1.1, -0.2), (1.1, 4)) → f
  16. Point({8, -2}) → fakeOrigin
  17. Sequence(Segment[fakeOrigin + ((gridSpacer * i), 0), fakeOrigin + ((gridSpacer * i), (10 * gridSpacer))], i, 1, 10) → verLines
  18. Sequence(Segment[fakeOrigin + (0, (gridSpacer * i)), fakeOrigin + ((gridSpacer * 10), (i * gridSpacer))], i, 1, 10) → horLines
  19. Vector(fakeOrigin, fakeOrigin + ((11 * gridSpacer), 0)) → xaxis
  20. Vector(fakeOrigin, fakeOrigin + (0, (11 * gridSpacer))) → yaxis
  21. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point2anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point2anchor), y(fakeOrigin)) * (1 - i / 300)) + (point2anchor * i / 300), i, 0, 300]}) → path2
  22. Element(path2, timer2) → mover2
  23. AreCollinear(point1anchor, point2anchor, point3anchor) → line
  24. Polygon((-0.3, -0.3), (2.5, -0.3), (2.5, 3.2), (-0.3, 3.2)) → region, h, i, j, k
  25. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point3anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point3anchor), y(fakeOrigin)) * (1 - i / 300)) + (point3anchor * i / 300), i, 0, 300]}) → path3
  26. Element(path3, timer3) → mover3
  27. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point1anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point1anchor), y(fakeOrigin)) * (1 - i / 300)) + (point1anchor * i / 300), i, 0, 300]}) → path1
  28. Element(path1, timer1) → mover1
  29. If(¬firstCheck, Line[mover1, mover2], Line[newMover1, newMover2]) → g
  30. Point({x(fakeOrigin) - gridSpacer, g(x(fakeOrigin) - gridSpacer)}) → leftBound
  31. Point({x(fakeOrigin) + (11 * gridSpacer), g(x(fakeOrigin) + (11 * gridSpacer))}) → rightBound
  32. If(¬firstCheck, Vector[mover1, leftBound], Vector[newMover1, leftBound]) → u
  33. If(¬firstCheck, Vector[mover1, rightBound], Vector[newMover1, rightBound]) → v
  34. If(¬firstCheck, timer3 ≟ Length[path3], checkedTimer ≟ 1) → ready

AI Drawing Prompt Reference

Draw a coordinate plane with grid lines and axes. Place three draggable anchor points on the grid, which determine a line. From the origin, draw paths to each anchor, with moving points along them. Based on whether the three anchors are collinear, show either a single line or two connecting segments. Overlay nine labeled points on the grid to detect their grid regions, outputting row and column indices. The whole figure demonstrates graphing a line via a table of values and verifying collinearity.
The prompt above was compiled from the original drawing commands and is for reference only.