Friday, January 8, 2010

How to calculate the gradient of a line?

for my Science coursework we need to calculate the line of the graphs we have drawn. So how do you do it? xHow to calculate the gradient of a line?
eqn of a line





y=mx+b





y and x are variables


b is the point the line crosses the y axis


m is the gradient and is calculated by any two points on the line (x1,y1) and (x2,y2) by:





m=(y2-y1)/(x2-x1)How to calculate the gradient of a line?
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The Two Point formula of a line is probably your best bet in this situation. All you need to do is to find two points that are easy to identify and use this formula:





(y-y₂)/(x-x₂) = (y₁-y₂)/(x₁-x₂) for points (x₁,y₁) and (x₂,y₂)





For example:


If your two points are


P₁(7,5) and P₂(6,-2) then





(y+2)/(x-6) = (5+2)/(7-6)


(y+2)/(x-6) = 7/1


.......... y+2 = 7(x-6)


.......... y+2 = 7x-42


.............. y = 7x -44





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NOTE


The right hand side of the formula is the slope of the line:


(y₁-y₂)/(x₁-x₂) = slope





Also, y = 7x -44 is in the Slope-Intercept


form y=mx+b where m=slope and b=y-intercept.


So y = 7x -44 has slope 7 and crosses the y=axis at -44.





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the difference of the 2 y divided bu the difference of the 2x





for example:





the 1st spot: (2,1)


the 2nd spot: (3,4)





subtract the Ys: 1 - 4


subtract the Xs: 2 - 3





the differences: y: -3


x: -1


= -3/-1 = 3





the gradient is 3
gradient line is also called a slope.


it's usually represented by m [not sure but that what i remember from my lesson]


if you want to see it here's the link.





http://www.mathsisfun.com/gradient.html

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