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:

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

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.