改变y截距如何影响线性关系

几何画板及绘图内容加载中，请稍等……

2019-02-05 21:42

①本范例演示了通过调整y截距如何改变直线在坐标系中的位置；②涉及的核心数学概念包括线性方程、斜率、y截距、坐标系；③作图要点——从下方『构造摘要』提炼用到了Textfield, LaTeX, If, Polygon等GeoGebra命令/对象；④适合初中及以上数学学习者，用于直观理解线性函数的性质和参数变化的影响。

GeoGebra 命令及参数

Textfield(textUserB) → ansBoxUserB
LaTeX(("\text{Given Line: }y=" * givenLine)) → givenLineLabel
If(numUserB > givenB, "crosses the \(y\)-axis\\higher", If[numUserB < givenB, "crosses the \(y\)-axis\\lower", If[numUserB ≟ givenB, "crosses the \(y\)-axis\\at the same place", "is invalid"]]) → result
LaTeX((("\fcolorbox{black}{#fff59d}{\text{Your line " * result) * ".}}")) → feedback
LaTeX(("\text{Your Line: }y=" * givenLine)) → userLineLabel
LaTeX("\text{\textbf{Question: }What is the relationship between the value of \(b\) and where the line crosses\\the \(y\)-axis?\\\textbf{Instructions: }Notice the equation of the line graphed below. Enter a new value for \(b\).\\What values of \(b\) result in a line that crosses the \(y\)-axis \textbf{higher} than the given line? What\\values of \(b\) result in a line that crosses the \(y\)-axis \textbf{lower}?}") → TEXT
Polygon((-17, -11), (-17, 21), (17, 21), (17, -11)) → viewBox, f, g, h, i