Thursday, December 24, 2009

What is the easiest way to work out the gradient of a straight line graph?

I haven't done this for ages and have forgotten, please help =PWhat is the easiest way to work out the gradient of a straight line graph?
Gradient = change in y over change in x in any given distance a long the line. The longer the distances, the more accurate it will be, if the line isn't a perfect y=2x kinda thing. Then where it crosses the y axis (c) makes the formula y=mx+c.What is the easiest way to work out the gradient of a straight line graph?
As Sandor says, you calculate the gradient of a function, not a graph - the graph is just a way of representing the function visually. So in general terms, if you were to draw the graph of the function f(x), where f(x) = ax^n, then the equation that gives the gradient for this function at any given point is found by taking the derivative of y with respect to x, written as d(y)/d(x).





In general terms, where f(x) = ax^n, then d(y)/d(x) = anx^(n-1); that is to say, multiply by the power and then subtract one from the power - so the derivative of x^2 is 2x, the derivative of x^3 is 3x^2, the derivative of 2x^2 - x = 4x - 1 and so on... hopefully you can see how to calculate these now. If one of the terms in the original function is purely numeric and has no value of x whatsoever, then this will disappear completely in taking the derivative. This new equation then allows you to find the gradient of the function at any point, just substitute in the value of x you require!





I hope that is understandable, I tried to stick to layman's terms as much as possible while also being thorough, I fear I may have fallen somewhere in between and achieved neither fully though...

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