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。
步骤
方法 1 的 4:
找出线性方程的斜率
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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
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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
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1
比如你有(x,y)形式的两点。 即 P1:(x1 ,y1 ) 和 P2(x2 ,y2 )。
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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。)
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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 “d ifference 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
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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。
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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。
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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。
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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。
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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)。