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Graphing Linear Relations from Slope and Y-Intercept

Graphing Linear Relations from Slope and Y-Intercept
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2018-12-04 03:39
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to graph a line using the slope and y-intercept. Key math concepts include linear equations. The construction summary mentions the use of GeoGebra commands such as Sequence, Polygon, Element, Zip, etc. Suitable for middle school and above students to learn how to graph linear equations.

GeoGebra Commands & Parameters

  1. Sequence((i, -3.65), i, 11.5, 12.5, 1) → homeBasePoints
  2. Polygon((-7, -7), (-7, 7), (7, 7), (7, -7)) → viewBox, f, g, h, i
  3. Element(questionList, questionListIndex) → questionNum
  4. Element(C2:C5, questionNum) → currentSlope
  5. Element(D2:D5, questionNum) → currentYIntercept
  6. Element(B2:B5, questionNum) → currentRun
  7. Element(A2:A5, questionNum) → currentRise
  8. Zip(A ≟ B, A, usersPreTaskValues, B, {currentSlope, currentYIntercept}) → arePreTasksCorrect
  9. DynamicCoordinates(freeA, If[IsInRegion[freeA, viewBox], x(freeA), x(Element[homeBasePoints, 1])], If[IsInRegion[freeA, viewBox], y(freeA), y(Element[homeBasePoints, 1])]) → A
  10. DynamicCoordinates(freeB, If[IsInRegion[freeB, viewBox], x(freeB), x(Element[homeBasePoints, 2])], If[IsInRegion[freeB, viewBox], y(freeB), y(Element[homeBasePoints, 2])]) → B
  11. FitPoly(usersPoints, 1) → usersLine
  12. Element(H2:H5, questionNum) → dottedCorrectLine
  13. UnicodeToLetter(10007) → xmark
  14. UnicodeToLetter(10003) → cmark
  15. LaTeX("\text{Points:}") → pointsLabel
  16. LaTeX("\text{Please plot all points.}") → feedbackPlotAllPoints
  17. Element(J2:J5, questionNum) → displayEquation
  18. Textfield(textPreTask1) → ansBoxPreTask1
  19. Textfield(textPreTask2) → ansBoxPreTask2
  20. Zip("\vphantom{\dfrac{\dfrac{1}{2}}{\dfrac{3}{4}}}" + (If[¬A, B, ""]), A, arePreTasksCorrect, B, {(((("\text{slope}=\dfrac{" * currentRise) * "}{") * currentRun) * "}"), ("y\text{-intercept}=" * currentYIntercept)}) → hints
  21. TableText({hints}, "v") → preTaskLabelHint
  22. Point({0, D2}) → E2
  23. Point({0, D3}) → E3
  24. Point({0, D4}) → E4
  25. Point({0, D5}) → E5
  26. Line(E2, F2) → H2
  27. Line(E3, F3) → H3
  28. Line(E4, F4) → H4
  29. Line(E5, F5) → H5
  30. Polygon(E2, F2, G2) → I2, g2, K2, L2
  31. Polygon(E3, F3, G3) → I3, J3_1, K3, L3
  32. Polygon(E4, F4, G4) → I4, J4_1, K4, L4
  33. Polygon(E5, F5, G5) → I5, J5_1, K5, L5
  34. Textfield(textPreTask3) → ansBoxPreTask3
  35. Element(I2:I5, questionNum) → slopeTriangle
  36. LaTeX("\text{A linear relation of the form\\\(y=mx+b\) has a slope of \(m\)\\and a \(y\)-intercept of \(b\).}") → feedbackPreTaskA
  37. LaTeX("\text{First rearrange the equation into\\the form \(y=mx+b\). Then, the\\linear relation will have a slope of\\\(m\) and a \(y\)-intercept of \(b\).}") → feedbackPreTaskB
  38. If(questionNum ≟ 1 ∨ questionNum ≟ 3, feedbackPreTaskA, feedbackPreTaskB) → feedbackPreTask
  39. LaTeX("\text{\textbf{Question: }Graph the linear relation by \textbf{first} calculating the slope and \(y\)-intercept.\\\textbf{Instructions: }Determine the slope and \(y\)-intercept. Then plot the \(y\)-intercept and one\\other point on the line by dragging points onto the grid.}") → TEXT
  40. TableText({{"\cellcolor{#ffcc80}{\text{slope}}"}, {(((("\dfrac{\vphantom{\frac{1}{2}}" * currentRise) * "}{\vphantom{\frac{1}{2}}") * currentRun) * "}")}, {"\cellcolor{#ffcc80}{y\text{-intercept value}}"}, {"\vphantom{\tfrac{1}{2}}" + currentYIntercept}}, "|_c") → preTaskLabel