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Revision:Gradients
From The Student RoomTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Gradients
Finding the gradient of a straight-line graphIt is often useful or necessary to find out what the gradient of a graph is - that is, a measure of how steep the line is. For a straight-line graph, you need to pick two points on the graph which you know the coordinates for.
ExampleFind the gradient of the line joining the points (1, 5) and (4, 11).
where m is the gradient.
which can be rearranged to get:
Finding the gradient of a curveIt is also possible to find the gradient of a curve at a given point - thought the gradient (steepness) will change as you move along the curve, so your answer will only be true for the gradient at the point you use. To find the gradient of a curve, you must draw an accurate sketch of the curve. At the point where you need to know the gradient, draw a tangent to the curve. A tangent is a straight line which touches the curve at one point only. You then find the gradient of this tangent like you did in the section above.
ExampleFind the gradient of the curve
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and
then the gradient is:
or
.

at the point (3, 9).





