线性函数基础：通过两点求斜率

几何画板及绘图内容加载中，请稍等……

2023-06-02 16:06

本范例演示了如何通过两个已知点确定一条线性函数的图像，并利用这两点计算直线的斜率。核心数学概念是线性函数、斜率以及两点式直线方程。作图要点包括：使用GeoGebra的Point命令创建点A和B，Line命令生成过两点的直线，Slope命令计算斜率并显示其数值；同时利用Shuffle和Element命令随机生成题目，Textfield和Button等交互组件提供输入验证与反馈。适合初中或高中阶段学习线性函数和斜率概念的课堂演示或自主练习，通过交互式操作帮助学生直观理解斜率的意义。

GeoGebra 命令及参数

Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {5, 2, 1, 7, 3, 4, 6}
Shuffle(Sequence[t, t, -6, 6, 1] \ {-1, 1}) → allCompX, {-2, 2, 6, -6, 5, 0, -5, 3, 4, -3, -4}
Shuffle(Sequence[t, t, -6, 6, 1] \ {0, -1, 1}) → allCompY, {-4, 6, 3, -5, 2, 4, -6, -3, -2, 5}
Shuffle(Join[Sequence[Sequence[(j, k), j, -10, 10, 1], k, -10, 10, 1]]) → bigGrid, {(0, -7), (-7, -7), (7, 5), (-6, 7), (2, 1), (1, -2), (-3, -9), (-5, 7), (-4, 3), (-3, 6), (2, -2), (-8, 0), (5, 7), (2, 3), (-8, 1), (10, -2), (4, 8), (-9, -4), (8, -6), (6, 5), (7, -7), (5, 8), (-3, 8), (-7, 9), (-2, 2), (5, 2), (10, -7), (2, -7), (0, -5), (4, 7), (-8, 4), (-4, -10), (9, 8), (8, -9), (-10, 8), (6, 1), (-3, -5), (-7, -9), (9, 5), (-8, -5), (8, 1), (6, 7), (-3, -2), (-9, -2), (-10, 5), (-10, -5), (5, 1), (10, 5), (0, 1), (8, 2), (1, -1), (9, 1), (4, -6), (-4, 10), (-8, 3), (-8, 5), (0, 5), (10, -4), (8, -2), (-8, -9), (2, 7), (0, 9), (8, 8), (3, -8), (5, -6), (4, 5), (-9, -10), (4, -1), (0, 6), (-4, -4), (-7, 5), (-2, 10), (-9, 2), (7, 4), (2, 9), (-8, 2), (7, 10), (-3, -10), (1, 6), (8, -5), (-1, 6), (1, -9), (8, -4), (4, 2), (1, -7), (-4, 5), (9, -8), (0, -2), (10, 7), (-2, -6), (4, -8), (9, -3), (2, 6), (-6, -8), (-10, -2), (-6, 1), (1, -4), (2, 5), (-6, -5), (-3, 10), (10, 9), (7, -1), (-7, 1), (10, -5), (-10, -8), (3, 7), (-10, 6), (9, -4), (6, -8), (-4, -9), (0, -10), (9, 9), (-10, 0), (8, -8), (4, -5), (7, -8), (-7, -1), (-5, 0), (-4, 9), (1, 5), (5, -9), (7, -2), (8, 7), (1, 2), (-10, -3), (-8, 8), (-7, 0), (5, -7), (-5, -7), (4, -3), (-9, 4), (3, -7), (3, 2), (8, -10), (-2, 1), (-5, 10), (-6, 3), (1, 10), (-1, -9), (-3, -1), (6, 4), (-2, 7), (3, -10), (-1, 5), (-9, 3), (-10, 3), (-2, -3), (-1, -1), (0, 4), (-3, 9), (4, -9), (-7, -4), (-9, -1), (-8, 9), (4, -7), (10, -3), (-3, 0), (4, -10), (-4, -2), (7, 1), (0, -8), (6, -1), (8, 6), (9, -5), (2, -6), (7, 6), (-9, 5), (-10, -1), (7, -4), (4, 3), (4, 6), (-6, -4), (6, 9), (-2, 8), (-9, 1), (-3, 1), (-1, 9), (-2, 5), (5, 9), (4, 1), (5, 3), (-2, 0), (8, 0), (5, 4), (6, -2), (-8, -10), (5, -4), (-5, 8), (-9, 8), (-7, 8), (-5, -2), (-4, 8), (-2, 4), (8, 3), (8, -7), (3, -5), (0, 3), (-3, -4), (-7, 10), (5, -5), (1, 7), (-1, 10), (3, -3), (-9, -9), (9, -1), (-9, 7), (2, -1), (0, -9), (-2, 3), (-7, -2), (6, -5), (0, 10), (-6, 8), (-7, -8), (1, -6), (5, -1), (1, -8), (-1, -5), (-10, -9), (-9, 9), (6, 0), (1, -10), (-3, -6), (8, 9), (-1, 1), (10, 6), (5, -3), (-10, 9), (-5, -6), (7, 3), (-3, -3), (-2, -10), (6, -3), (-1, 0), (0, 7), (0, -6), (-4, 4), (-6, 6), (4, -2), (6, -7), (9, 7), (5, 5), (-7, 6), (-1, 2), (4, 9), (10, 4), (-7, 4), (10, 0), (-10, -6), (3, 3), (-6, 2), (-4, 6), (-6, -3), (-9, -8), (-9, 0), (6, 6), (9, 3), (-10, 1), (6, -9), (-6, 5), (-2, 9), (6, -4), (10, -9), (1, 9), (-6, -10), (-4, 2), (-10, 7), (4, -4), (-7, 7), (-3, 4), (-8, -2), (9, -2), (6, 3), (9, 10), (-7, -10), (-5, -3), (-5, 9), (1, 4), (0, 8), (0, 2), (-6, -1), (5, 6), (-1, -8), (-5, -8), (-2, -1), (-6, -7), (1, 8), (-4, -5), (5, -10), (-9, -3), (5, -2), (-5, 6), (7, -10), (7, 0), (-4, -7), (-8, -3), (-1, -6), (10, 8), (2, -8), (-6, -9), (4, 4), (-5, -5), (-10, 10), (-9, 10), (9, -10), (0, -4), (1, -3), (5, 0), (2, -10), (-6, 10), (-8, -7), (3, -2), (-3, 2), (10, 3), (7, -5), (-8, 6), (-6, 9), (-5, 3), (2, 10), (2, 8), (-3, -7), (-5, 2), (-3, 7), (7, -9), (3, 9), (-4, 0), (7, 2), (-7, -5), (-9, 6), (6, 8), (-2, -2), (6, -6), (10, 2), (8, 4), (10, -10), (5, -8), (-6, -2), (0, -1), (3, 10), (-5, 1), (3, -1), (0, -3), (-3, 3), (-7, -6), (-1, -10), (8, -3), (9, -9), (2, 2), (6, 2), (-1, 3), (-6, 4), (10, 10), (-8, -4), (-10, -7), (2, 4), (1, 0), (-10, -10), (2, -5), (-6, -6), (3, 6), (-1, 8), (-1, -7), (-5, -4), (-7, 2), (2, -3), (2, 0), (-2, -9), (3, -4), (-9, -6), (8, 10), (-10, -4), (-2, -5), (3, 5), (9, -6), (5, 10), (-5, 5), (-4, -8), (-6, 0), (-8, 7), (9, 4), (-2, 6), (-8, -8), (-2, -7), (7, -6), (-1, 4), (1, 3), (-10, 4), (-4, -3), (-3, -8), (3, 4), (-4, 1), (-7, -3), (-4, -6), (7, -3), (1, -5), (3, 1), (1, 1), (2, -4), (-2, -8), (-2, -4), (-3, 5), (9, -7), (6, 10), (6, -10), (-8, 10), (4, 0), (-10, 2), (-8, -1), (10, 1), (4, 10), (-7, 3), (9, 2), (3, -6), (-4, -1), (10, -8), (-8, -6), (-5, -9), (10, -6), (3, -9), (-5, -1), (7, 9), (8, 5), (-1, 7), (9, 6), (-4, 7), (3, 8), (-1, -2), (7, 8), (-1, -4), (-9, -7), (-1, -3), (3, 0), (-9, -5), (2, -9), (7, 7), (10, -1), (8, -1), (-5, 4), (0, 0), (-5, -10), (9, 0)}
Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
Element(allCompX, Mod[countQuestion, Length[allCompX]] + 1) → compX
Element(allCompY, Mod[countQuestion, Length[allCompY]] + 1) → compY
Element(bigGrid, Mod[countQuestion, Length[bigGrid]] + 1) → V1
Point(bigGrid) → A
Point(bigGrid) → B
Line(A, B) → lineAB
Slope(lineAB) → mAB
Textfield(inputB) → InputBoxB
Corner(5) → layoutAppSize
onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
Textfield(inputA) → InputBoxA
Textfield(inputC) → InputBoxC
Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, f, g, h, i
Segment((-10.8, 0), (10.8, 0)) → fakeX
Segment((0, -10.8), (0, 10.8)) → fakeY
Vector(V1, (0, 0)) → aniVec
Translate(V1, Vector[(aniSli * aniVec)]) → V1T
Translate(V2, Vector[(aniSli * aniVec)]) → V2T
Vector((10, 0), (11.2, 0)) → arrowX
Vector((0, 10), (0, 11.2)) → arrowy
If(y(A) > y(B), (x(A), y(B)), (x(B), y(A))) → C
If(y(A) > y(B), Segment[B, B + (aniSli * (C - B))], Segment[A, A + (aniSli * (C - A))]) → horProj
If(y(A) > y(B), Segment[A, A + (aniSli * (C - A))], Segment[B, B + (aniSli * (C - B))]) → vertProj

AI 绘图提示语参考

这是一个线性函数活动图形，包含两个随机点、连接它们的线、斜率计算结果、输入框用于输入斜率答案、随机点对生成、水平投影线和垂直投影线、多边形用于显示坐标轴、线段用于显示坐标轴范围。构造顺序：先生成随机点对，创建两个点，连接线，计算斜率，创建输入框，设置布局，创建多边形，创建坐标轴线段，进行向量操作，创建投影线。

以上提示语为根据原始绘图命令整理而来，仅供参考。