Find slope angle of a line

Question

How does one find the slope of a graph line using multiple coordinates. I know how to find slope using two coordinates of the line. In this case i want to find the slope of a line using several coordinates say 6 coordinates.

Answer 1

If there are 6 coordinates $ A(x_1,y_1);\,B(x_2,y_2);\,C(x_3,y_3)$ on a curved line then the slope of secant $AB$ can be found by the straight line equation you know.

Using the same you can find other separate slopes of secants $BC$ and $ CA.$ A finite difference polynomial can be built summing up forward/backward differences.

Answer 2

Recall that, slope is a derivative of a continuous function within a range (a,b), where

1. $f$ is defined on closed interval $[a,b]$
2. $f$ is smooth or derivable means holds continuity of $]a,b[$

where,

• $]~~[$ - denotes open interval all the points except a and b,

• $[~~]$ - denotes all the points in the interval including the extreme boundary points.

Satisfying the above conditions, slope is derivative at any interstitial points is defined as

$f(x) = \frac{df}{dx} = \lim_{h \to 0} f(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$