Jameson开车速度与距离关系示例

GeoGebra 命令及参数

1. LaTeX("\text{Identify the independent and dependent quantities.}") → Text1_1
2. LaTeX((("\text{\textcolor{#000099}{d}=\textcolor{#000099}{" * d0) * "}}")) → Text4_{12}
3. LaTeX((("\text{\textcolor{#000099}{d}=\textcolor{#000099}{" * d1) * "}}")) → Text4_{17}
4. Segment(F, E) → i
5. Segment(E, G) → j
6. Segment(G, H) → k
7. Segment(F, H) → l
8. Midpoint(i) → I
9. Midpoint(k) → K
10. Point(j) → J
11. Point(l) → L
12. Point(j) → M
13. Point(l) → N
14. Point(j) → O
15. Point(l) → P
16. Point(j) → Q
17. Point(l) → R
18. Point(j) → S
19. Point(l) → T
20. Point(j) → U
21. Point(l) → V
22. Polygon(A_1, B_1, C_1, D_1) → poly1, a_1, b_1, c_1, d_1
23. Sequence(Segment[(19, 490 + (80 * i)), (34, 490 + (80 * i))], i, 0, 6) → LinesHori
24. Segment(A6, F6) → a
25. LaTeX("\text{Use the buttons below to return to the original problem or}") → Check_1
26. LaTeX("\text{randomly generate a similar practice problem. }") → Check_2
27. FitLineY({E6, D6}) → b
28. Intersect(b, yAxis) → E_1
29. Segment(G_1, H_1) → c_2
30. Segment(G_1, I_1) → d
31. Segment(H_1, J_1) → e
32. Segment(I_1, J_1) → f
33. Point(d) → K_1
34. Point(e) → L_1
35. Point(d) → M_1
36. Point(e) → N_1
37. Point(d) → O_1
38. Point(e) → P_1
39. Point(d) → Q_1
40. Point(e) → R_1
41. Point(d) → S_1
42. Point(e) → T_1
43. Point(c_2) → Z_1
44. Point(f) → A_2
45. VerticalText("\text{Total distance in miles \textcolor{#000099}{(d)}") → text2
46. LaTeX("{x}") → text1
47. LaTeX("{y}") → text1_1
48. LaTeX("\text{Distance Traveled over Time}") → text1_3
49. FitLineY({A6, E_1}) → t
50. FitLineY({A6, E_1}) → e_1
51. FitLineY({A6, E_1}) → f_1
52. FitLineY({A6, E_1}) → g_1
53. FitLineY({A6, E_1}) → h_1
54. FitLineY({A6, E_1}) → j_1
55. FitLineY({B6, F6}) → s
56. Point(yAxis) → F_1
57. OrthogonalLine(F_1, s) → i_1
58. Intersect(s, i_1) → E_2
59. Intersect(s, yAxis) → F_2
60. Vector(F_2, E_2) → u
61. LaTeX("\text{the total distance also increases.}") → Text4_{21}
62. Point(d) → U_1
63. Point(e) → V_1
64. LaTeX((((("\text{The values in the second row will be \textcolor{#000099}{" * val1) * "} and \textcolor{#000099}{") * d1) * "}.}")) → Text4_{18}
65. LaTeX("\text{Time in hours \textcolor{#000099}{(t)}") → text1_2
66. LaTeX("\text{Choose variables to represent the independent and dependent quantities.}") → Text2_1
67. LaTeX("\text{Create an equation, a table, and a graph to explore the relationship between the total distance that }") → Question1
68. LaTeX("\text{traveled depends on the time in hours that he spent driving.}") → Text1_3
69. LaTeX("\text{Since “distance” starts with the letter “\textcolor{#000099}{d},” let the distance be represented by the variable \textcolor{#000099}{d}.}") → Text2_3
70. LaTeX("\text{Write an equation to represent the relationship between the independent and dependent variables.}") → Text3_1
71. LaTeX("\text{by the time in hours \textcolor{#000099} {(t)} that he spent driving.}") → Text3_4
72. LaTeX("\text{Create a table of values to represent the relationship between the independent and dependent variables. }") → Text4_1
73. LaTeX("\text{Use the table to create a graph that represents the relationship between the independent and dependent variables. }") → Text5_1
74. LaTeX("\text{plane to represent the relationship.}") → Text5_{13}
75. LaTeX("\text{Each row in the table of values provides a coordinate point that can be graphed on the coordinate }") → Text5_{12}
76. LaTeX("\text{coordinate points to show how the total distance traveled was constantly changing.}") → Text5_{19}
77. LaTeX("\text{This graph shows that as the time }") → Text5_{25}
78. LaTeX("\text{shown in the table of values.}") → Text5_2
79. Polygon(A_3, G_2, J_2, K_2) → poly2, a_2, g_2, j_2, k_2
80. TableText({{"Time \;in\; hours \;\textcolor{#000099}{(t)}", LaTeX[(("\text{ \textcolor{#000099}{" * val0) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * val1) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * val2) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * val3) * "} }")], LaTeX[(("\text{\textcolor{#000099}{ " * val4) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * val5) * "} }")]}, {"Total\; distance\; in\; miles \;\textcolor{#000099}{(d)}", LaTeX[(("\text{\textcolor{#000099}{ " * d0) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * d1) * "} }")], LaTeX[(("\text{ \textcolor{#000099}{" * d2) * "} }")], LaTeX[(("\text{\textcolor{#000099}{ " * d3) * "} }")], LaTeX[(("\text{\textcolor{#000099}{" * d4) * "} }")], LaTeX[(("\text{\textcolor{#000099}{ " * d5) * "} }")]}}, "hc|_") → text3
81. LaTeX((("\text{Jameson traveled and the time that he spent driving at an average speed of \textcolor{#000099}{" * miles1) * " } miles per hour. }")) → Question1_2
82. LaTeX((("\text{Miles per hour=" * miles1) * "}")) → text5
83. LaTeX("\text{Since “time” starts with the letter “\textcolor{#000099}{t},” let the time be represented by the variable \textcolor{#000099}{t}.}") → Text2_2
84. LaTeX("\text{Since Jameson drove at a constant rate of speed,and since it is possible for Jameson to drive for a fractional }") → Text5_{21}
85. LaTeX("\text{The title of the graph can be “Distance Traveled over Time.” }") → Text5_5
86. LaTeX((("\text{The distance in miles \textcolor{#000099}{(d)} that Jameson traveled is calculated by multiplying his rate (\textcolor{#000099}{" * miles1) * "} miles per hour) }")) → Text3_3
87. LaTeX((("\text{\textcolor{#000099}{d}=\textcolor{#000099}{" * miles1) * "t}}")) → Text4_{10}
88. LaTeX((((("\text{\textcolor{#000099}{d}=\textcolor{#000099}{" * miles1) * "( ") * val0) * ")}}")) → Text4_{11}
89. LaTeX((((("\text{\textcolor{#000099}{d}=\textcolor{#000099}{" * miles1) * "( ") * val1) * ")}}")) → Text4_{16}
90. LaTeX((("\text{Jameson drove his car at \textcolor{#000099}{" * miles1) * "} miles per hour, which means that the total distance in miles that Jameson }")) → Text1_2
91. LaTeX("\text{Therefore, the time is the independent quantity, and the distance is the dependent quantity.}") → Text1_4
92. LaTeX((("\text{Therefore, the relationship can be represented by the equation \textcolor{#000099}{d}=\textcolor{#000099}{" * miles1) * "t}.}")) → Text3_5
93. LaTeX("\text{Use one row of the table for the values of the independent variable, the time in hours \textcolor{#000099}{(t)}.}") → Text4_2
94. LaTeX("\text{Use the other row of the table for the values of the dependent variable, the total distance in miles \textcolor{#000099}{(d)}.}") → Text4_5
95. LaTeX((("\text{To fill in the table, choose values for \textcolor{#000099}{t} to substitute into the equation \textcolor{#000099}{d}=\textcolor{#000099}{" * miles1) * "t}. Let’s start with \textcolor{#000099}{0}.}")) → Text4_7
96. LaTeX((("\text{For the first row of the table, let \textcolor{#000099}{t=" * val0) * "}:}")) → Text4_9
97. LaTeX((((("\text{So, the values in the first row will be \textcolor{#000099}{" * val0) * "} and \textcolor{#000099}{") * d0) * "}.}")) → Text4_{13}
98. LaTeX((("\text{For the second row of the table, let \textcolor{#000099}{t=" * val1) * "}:}")) → Text4_{14}
99. LaTeX("\text{Continue with other values of \textcolor{#000099}{t}, as shown.}") → Text4_{20}
100. LaTeX("\text{Based on the table, as the time increases,}") → Text4_{15}
101. LaTeX("\text{The independent quantity, the time in hours \textcolor{#000099}{(t)}, is plotted along the \textcolor{#000099}{x}-axis of the coordinate plane. }") → Text5_3
102. LaTeX("\text{The dependent quantity, the total distance in miles \textcolor{#000099}{(d)}, is plotted along the \textcolor{#000099}{y}-axis. }") → Text5_4
103. LaTeX((("\text{Since it is not possible to have a negative amount of time, the \textcolor{#000099}{x}-axis starts at \textcolor{#000099}{" * val0) * "}. Since it is not possible to}")) → Text5_6
104. LaTeX((("\text{travel a negative distance, the \textcolor{#000099}{y}-axis also starts at \textcolor{#000099}{" * val0) * "}.}")) → Text5_8
105. LaTeX("\text{number of hours (such as \textcolor{#000099}{2.5} hours) instead of only a whole number of hours, draw a line through the}") → Text5_{23}
106. LaTeX("\text{increases, the total distance traveled also }") → Text5_{26}
107. LaTeX("\text{increases. This confirms the relationship }") → Text5_{27}
108. LaTeX("\text{\textbf{dependent variable}\;labeled on the y-axis; the quantity that is based on the}") → text6_2
109. LaTeX("\text{\textbf{independent variable}\;labeled on the x-axis; the quantity that changes based}") → text6
110. LaTeX("\text{input values of the independent variable; the output variable of a function}") → text6_3
111. LaTeX("\text{on values chosen; the input variable of a function}") → text6_1