#1 (permalink)

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#2 (permalink)

The gradient of a line (also known as slope...I will probably slip up and use the term "slope" in this post, because it is what I was taught it as.) is simply a way to describe lines.

The simplest way to describe it would be the (change in) y/ (change in) x

For the example you have shown above, the formula to find the slope would be (y2-y1)/(x2-x1)

#3 (permalink)

http://i66.photobucket.com/albums/h2...damj/slope.jpg

Basically, its rise/run.

I've never really heard the word "gradient" used at all, usually I hear "slope".

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www.last.fm/user/shmads/

#4 (permalink)

Oh kay.

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#5 (permalink)

The word gradient means slope.

The slope of a line is the ratio of the change in y divided the change in x. The word "change" in this case indicates subtraction.

Simply put, find the difference of both y and x coordinates and place them in a ratio.

Pick two points on any given line. Because you are using two sets of ordered pairs both having x and y values, a subscript must be used to distinguish between the two values.

The subscribts are given as points to distinguish between the two points on a line.

Here are the subscribts normally found in math books:

(x1, y1) = a point on the line

(x2, y2) = a point on the line

However, you don't have to use the subscribts shown here to find the slope or gradient.

You can use any letters as subscribts.

I like to use the letters a, b, c and d this way:

(a, b) = one point

(c, d) = one point

The slope or gradient is simply (d - b)/(c - a).

The letter M has been used to represent the slope equation.

Again, I'd say use any letter of choice.

Whatever is easier for you.

In fact, it makes more sense to use the letter S (for slope) or G (for gradient).

You can use either equation below to find the slope or gradient:

S = (d - b)/(c - a)

or

G = (d - b)/(c - a)

Here is an example:

Find the gradient (or the slope) of the line having the following two points: (3, -1) and (4, 0).

I will use S = (d - b)/(c - a).

Look at the points given.

Here, a = 3, b = -1, c = 4 and d = 0

We now plug and chug.

S = (0 - (-1))/(4 - 3)

S = 1/1

S = 1....The slope or gradient of this line is 1.

Did you follow?