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直线函数图示例

直线函数图示例
几何画板及绘图内容加载中，请稍等……
2015-11-10 03:10
函数解析几何函数图像
所属专题 CCSS Support Algebra I Unit 3
本示例展示了直线函数的图像。通过选取直线上两点，利用斜率公式 [math]m= rac{y_2-y_1}{x_2-x_1}[/math] 计算斜率，并写出直线方程。使用了SelectedElement, Polygon, LaTeX, Segment, Division, FractionText等GeoGebra命令。适合初中及以上学生学习直线函数的相关概念。

GeoGebra 命令及参数

  1. SelectedElement(FXX) → FXXV
  2. SelectedElement(FXC) → FXCV
  3. SelectedElement(GXX) → GXXV
  4. SelectedElement(GXC) → GXCV
  5. Polygon(H, I, J, K) → poly1, h, i, j, k
  6. LaTeX("\text{Determine the slope of the line.}") → text14
  7. LaTeX("\text{into the slope formula.}") → text18
  8. LaTeX("\text{Use the point-slope form to write the equation for this line.}") → text25
  9. LaTeX("\text{to write the point-slope form of this line.}") → text29
  10. LaTeX("\text{in the point-slope form.}") → text31
  11. LaTeX("\text{Rewrite the equation in slope-intercept form.}") → text38
  12. LaTeX("\text{of the equation.}") → text53
  13. Segment(R, T) → a
  14. LaTeX("\text{x₁:}") → DKT1
  15. LaTeX("\text{y₁:}") → DKT2
  16. LaTeX("\text{x₂:}") → DKT3
  17. LaTeX("\text{y₂:}") → DKT4
  18. LaTeX("\text{The graph of a linear function is shown.Use two points on the line") → text1
  19. LaTeX("\text{for this line using the point-slope form,\textcolor{#000099}{y−y₁=m(x−x₁)}.}") → text11
  20. LaTeX("\text{Then,rewrite the result in slope-intercept form,\textcolor{#000099}{y=mx+b}.}") → text12
  21. LaTeX("\text{Use the slope-intercept form to determine the \textcolor{#000099}{y}-intercept,\textcolor{#000099}{b}.}") → text13
  22. LaTeX("\text{Use two points on the line to determine the slope.Two easily identifiable}") → text15
  23. LaTeX((((((((("\text{points on the line are \textcolor{#000099}{(" * FXXV) * ", ") * FXCV) * ")} and \textcolor{#000099}{(") * GXCV) * ", ") * GXXV) * ")}.}")) → text16
  24. LaTeX((((((((("\text{Let \textcolor{#000099}{(x₁,y₁)} be \textcolor{#000099}{(" * FXXV) * ", ") * FXCV) * ")} and \textcolor{#000099}{(x₂,y₂)} be \textcolor{#000099}{(") * GXCV) * ", ") * GXXV) * ")}.Substitute these values}")) → text17
  25. LaTeX((((((((("\text{\textcolor{#000099}{m=}}{\textcolor{#000099}{\frac{(" * GXXV) * ")−(") * FXCV) * ")}{(") * GXCV) * ")−(") * FXXV) * ")}}}")) → text20
  26. LaTeX((((((("\text{Substitute \textcolor{#000099}{" * GXXV) * "} for \textcolor{#000099}{y₂},\textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y₁},\textcolor{#000099}{") * GXCV) * "} for \textcolor{#000099}{x₂},}")) → text21
  27. LaTeX((("\text{and \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x₁}.}")) → text22
  28. LaTeX((((("\text{The given line has a slope of }{\textcolor{#000099}{\frac{" * numupdate) * "}{") * denupdate) * "}}.}")) → text24
  29. LaTeX("\text{The point-slope form of a linear function is \textcolor{#000099}{y−y₁=m(x−x₁)},where}") → text26
  30. LaTeX("\text{\textcolor{#000099}{m} is the slope and \textcolor{#000099}{(x₁,y₁)} is a point on the line.}") → text27
  31. LaTeX((((((((("\text{Substitute the point \textcolor {#000099} {(" * FXXV) * ",") * FXCV) * ")} for \textcolor{#000099}{(x₁,y₁)} and substitute the slope }\textcolor{#000099}{{\frac{") * numupdate) * "}{") * denupdate) * "}}}\text{ for \textcolor{#000099}{m}}")) → text30
  32. LaTeX("\text{\textcolor{#000099}{y−y₁=m(x−x₁)} Point-slope form}") → text32
  33. LaTeX((((((((("\text{The equation of the line in point-slope form is \textcolor{#000099}{y−" * FXCV) * "={ \frac{") * numupdate) * "}{") * denupdate) * "}}(x−") * FXXV) * ")}.}")) → text37
  34. LaTeX("\text{The slope-intercept form of a linear function is \textcolor{#000099}{y=mx+b},where \textcolor{#000099}{m} is}") → text39
  35. LaTeX("\text{the slope and \textcolor{#000099}{b} is the \textcolor{#000099}{y}-intercept.}") → text40
  36. LaTeX("\text{the equation for \textcolor{#000099}{y} and simplify.}") → text42
  37. LaTeX("\text{Determine the \textcolor{#000099}{y}-intercept of the line.}") → text47
  38. LaTeX("\text{This equation is in slope-intercept form,\textcolor{#000099}{y = mx + b},where \textcolor{#000099}{m}\ is the}") → text49
  39. LaTeX("\text{slope and \textcolor{#000099}{b} is the \textcolor{#000099}{y}-intercept.}") → text50
  40. LaTeX("\text{\textcolor{#000099}{m=}}{\textcolor{#000099}{\frac{y₂−y₁}{x₂−x₁}}}{\text{ Slope formula}}") → text19
  41. LaTeX((((((((("\text{The \textcolor{#000099}{y}-intercept can be determined from the equation}\textcolor{#000099}{\text{ y=} {\frac{" * numupdate) * "}{") * denupdate) * "}}\text{x+{\frac{") * ssimpnum) * "}{") * denupdate) * "}}}.}")) → text48
  42. LaTeX((((((((("\text\textcolor{#000099}{{y=} {\frac{" * numupdate) * "}{") * denupdate) * "}}\text{x+{\frac{") * ssimpnum) * "}{") * denupdate) * "}}}}")) → text45
  43. LaTeX((("\text{Add \textcolor{#000099}{" * FXCV) * "} to both sides to isolate \textcolor{#000099}{y}.}")) → text45_1
  44. LaTeX((((((("\text{Distribute\textcolor{#000099}{{ \frac{" * numupdate) * "}{") * denupdate) * "}}} \text{over \textcolor{#000099}{x−") * FXXV) * "}.}}")) → text441
  45. LaTeX((((((((((("\text{\textcolor{#000099}{{y−" * FXCV) * "=} { \frac{") * numupdate) * "}{") * denupdate) * "}}\text{x−{\frac{") * simpnum) * "}{") * denupdate) * "}}}}")) → text44
  46. LaTeX("\text{Point-slope form of the line}") → text431
  47. LaTeX((((((((("\text{\textcolor{#000099}{{y−" * FXCV) * "=} { \frac{") * numupdate) * "}{") * denupdate) * "}}\text{(x−") * FXXV) * ")}}")) → text43
  48. LaTeX("\text{Simplify.}") → text361
  49. LaTeX((((((((("\text{\textcolor{#000099}{y−" * FXCV) * "={ \frac{") * numupdate) * "}{") * denupdate) * "}}(x−") * FXXV) * ")}}")) → text36
  50. LaTeX("\text{Simplify.}") → text231
  51. LaTeX((((("\text{\textcolor{#000099}{m=}}{\textcolor{#000099}{\frac{" * numupdate) * "}{") * denupdate) * "}}}")) → text23
  52. LaTeX((((((((((((("\text{Use either one of the points,\textcolor{#000099}{(" * FXXV) * ",") * FXCV) * ")} or \textcolor{#000099}{(") * GXCV) * ",") * GXXV) * ")},along with the slope,}{\textcolor{#000099}{\frac{") * numupdate) * "}{") * denupdate) * "}},}")) → text28
  53. LaTeX((((((((("\text{\textcolor{#000099}{y−(" * FXCV) * ")={\left( \frac{") * numupdate) * "}{") * denupdate) * "} \right)}[x−(") * FXXV) * ")]}}")) → text33
  54. LaTeX((((((((("\text{To write the equation \textcolor{#000099}{y−" * FXCV) * "={ \frac{") * numupdate) * "}{") * denupdate) * "}}(x−") * FXXV) * ")}}\text{ in slope-intercept form,solve}")) → text41
  55. Division(ssimpnum, denupdate) → checkfrac1
  56. FractionText(displayfrac) → text54
  57. FractionText(displayfrac) → text55
  58. LaTeX((("\text{the \textcolor{#000099}{y}-axis at approximately \textcolor{#000099}{" * Element[checkfrac1, 1]) * "} ,so this verifies the slope‑intercept form}")) → text52
  59. LaTeX((((((("\text{Substitute \textcolor{#000099}{" * FXCV) * "} for \textcolor{#000099}{ y₁},}{\textcolor{#000099}{\frac{") * numupdate) * "}{") * denupdate) * "}}\text{for \textcolor{#000099}{m},}")) → text34
  60. LaTeX((("\text{and \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x₁}.}")) → text35
  61. LaTeX("\text{method,draw a line using only two points on the coordinate plane.}") → text3
  62. LaTeX((((((((("\text{The equation of the line in slope-intercept form is}\textcolor{#000099}{\text{ y=} {\frac{" * numupdate) * "}{") * denupdate) * "}}\text{x+{\frac{") * ssimpnum) * "}{") * denupdate) * "}}.}")) → text46
  63. LaTeX((((((("\text{The \textcolor{#000099}{y}-intercept is \textcolor{#000099}{{\frac{" * ssimpnum) * "}{") * denupdate) * "}}},or \textcolor{#000099}{") * Element[checkfrac1, 1]) * "} .Note that on the graph the line crosses}")) → text51
  64. Polygon(U, V, W, Z) → poly2, u_1, v_1, w, z_1
  65. Polygon(B_1, C_1, D_1, E_1) → poly3, b_1, c_1, d_1, e_1
  66. LaTeX("\text{\mathbf{Slope}-\mathbf{intercept\;method} the method used to graph a linear equation;with this }") → text2
  67. LaTeX("\text{\mathbf{\textcolor{#000099}{y}}-\mathbf{intercept} the point at which the graph crosses the \textcolor{#000099}{y}-axis;written as \textcolor{#000099}{(0, y)}.}") → text4

AI 绘图提示语参考

画一个直线函数的图像，通过选择直线上两个点来确定斜率，使用点斜式方程 y - y₁ = m(x - x₁) 写出直线方程，然后将其转换为斜截式 y = mx + b。首先，选择直线上两个点，计算斜率 m = (y₂ - y₁) / (x₂ - x₁)，接着使用点斜式方程写出直线方程，最后简化为斜截式方程。
以上提示语为根据原始绘图命令整理而来，仅供参考。