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从斜率和截距绘制线性关系

从斜率和截距绘制线性关系
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2018-12-04 03:39
函数解析几何几何作图
本范例演示如何使用斜率和截距绘制直线。核心数学概念包括线性方程。构造摘要中提到了使用Sequence, Polygon, Element, Zip等GeoGebra命令。适合初中及以上学生学习线性方程的绘制方法。

GeoGebra 命令及参数

  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