怎么求得一个方程的斜率

想求直线方程的斜率?下面教你用多种方法求出个各种直线的斜率。

方法 1 的 4:

找出线性方程的斜率

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/c\/c7\/Find-the-Slope-of-an-Equation-Step-1.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-1.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/c\/c7\/Find-the-Slope-of-an-Equation-Step-1.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 如果有 (x,y)变量的二元一次方程,就通过加减、乘除法来整理得到斜截式: y = mx + b
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/be\/Find-the-Slope-of-an-Equation-Step-2.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/be\/Find-the-Slope-of-an-Equation-Step-2.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 m,即x的系数,就是方程的斜率。m这个变量可以很好记,想象一个上山(mountain, "m")的斜坡,或者想象屋顶(roof,"r")的倾斜度。
方法 2 的 4:

通过两点找出斜率

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d9\/Find-the-Slope-of-an-Equation-Step-3.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d9\/Find-the-Slope-of-an-Equation-Step-3.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 比如你有(x,y)形式的两点。即 P1:(x1,y1) 和 P2(x2,y2)。
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/0\/09\/Find-the-Slope-of-an-Equation-Step-4.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/0\/09\/Find-the-Slope-of-an-Equation-Step-4.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 斜率就是竖直变化除以横向变化:就是用坐标上升量除以坐标右移量。“竖直变化”就是y坐标值的变化(Y轴是竖直方向的),横向变化值,就是坐标右移变化量。(X轴是水平方向的。)
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/2a\/Find-the-Slope-of-an-Equation-Step-5.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-5.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/2a\/Find-the-Slope-of-an-Equation-Step-5.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 因此斜率的等式是 (y2 - y1)/(x2 - x1)。可以用希腊字母 “Δ”(“delta”)表示 ,它的意义是 “difference of”(差值)。因此斜率可以表示为 Δy/Δx,意为 "y 坐标变化/ x坐标变化"。
方法 3 的 4:

找出竖直方向或水平方向线的斜率

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/14\/Find-the-Slope-of-an-Equation-Step-6.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-6.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/14\/Find-the-Slope-of-an-Equation-Step-6.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 任何时候,水平方向线的斜率都是0 。为什么?这是因为y坐标的变化量为零。因此Δy = 0,则 Δy/Δx = 0。
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6f\/Find-the-Slope-of-an-Equation-Step-7.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-7.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6f\/Find-the-Slope-of-an-Equation-Step-7.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 任何时候,竖直方向的线斜率都不存在。为什么?这是因为x坐标变化量为零。因此 Δx = 0,因此 Δy/Δx 没有实数意义。
方法 4 的 4:

用微分计算曲线切线斜率

这部分数学比上面的部分要高深的多。如果你还没有上过微积分课,就可能看不懂这部分,也对你没有什么用处。

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/61\/Find-the-Slope-of-an-Equation-Step-8.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-8.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/61\/Find-the-Slope-of-an-Equation-Step-8.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 你已经知道,微分方程可以告诉你某点的斜率。
    • 换句话说, f’(x) = 是方程在 (x,f(x))的斜率。
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/55\/Find-the-Slope-of-an-Equation-Step-9.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-9.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/55\/Find-the-Slope-of-an-Equation-Step-9.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 把f(x) 整理到等号一边,这样另一边只有常数项和x项了。然后求微分。
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f0\/Find-the-Slope-of-an-Equation-Step-10.jpg\/v4-460px-Find-the-Slope-of-an-Equation-Step-10.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f0\/Find-the-Slope-of-an-Equation-Step-10.jpg\/v4-728px-Find-the-Slope-of-an-Equation-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 想要找出某个点的切线斜率,将x代入 f’(x)。
    • 因此想要找出 x = k 的斜率,带进k,得到 f’(k)。

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