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The Gradient Function

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Introduction

The Gradient Function

x=a’ is a vertical line which intercepts the x-axis at point ‘a’.

‘y=a’ is a horizontal line which will intercept the y-axis at point ‘a’.

‘y=ax’ and ‘y=-ax’ are the equations for a sloping line which intercepts at the origin. The value of ‘a’ is the gradient of the line, so therefore the larger the value of ‘a’ the steeper the gradient of the line.

I am trying to find the gradient function this is a formula that will work out the gradient of any line.

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Middle

x

-3

-2

-1

0

1

2

3

x2

9

4

1

0

1

4

9

y

9

4

1

0

1

4

9

(See graph, fig.1)

From the graph we can see that as the values of the coordinates increases, so does the gradient. We can see this from the

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Conclusion

‘y’ value’s by squaring the ‘x’ value. The closer the two points the more accurate the result will be, for example if we choose ‘2’ as the first ‘x’ value we could then choose ‘2.001’ as the next ‘x’ value. The gradient is found using the equation:

Gradient=y1-y2

                                                     x1-x2

So using the example numbers from above I would find the gradient as shown below:

Gradient=y1-y2

                                                     x1-x2

=4.004001-4

2.001-2

Gradient =4.001

This method is more accurate than using the results from the graph. This is because when taking results from the graph it is very difficult to get them as precise.

...read more.

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