Note:
If the gradient of a line is negative, then the line slopes
downward as the value of x increases.
Applications of Gradients
Gradients are an important part of life. The roof of a house is built
with a gradient to enable rain water to run down the roof. An aeroplane
ascends at a particular gradient after take off, flies at a different
gradient and descends at another gradient to safely land. Tennis courts,
roads, football and cricket grounds are made with a gradient to assist
drainage.
Example 5
A horse gallops for 20 minutes and covers a distance of 15 km, as shown
in the diagram.
Find the gradient of the line and describe its meaning.
Solution:
In the above example, we notice that the gradient of the distance-time
graph gives the speed (in kilometres per minute); and the distance covered
by the horse can be represented by the equation:
Example 6
The cost of transporting documents by courier is given by the line
segment drawn in the diagram. Find the gradient of the line segment; and
describe its meaning.
Solution:
So, the gradient of the line is 3. This means that the cost of
transporting documents is $3 per km plus a fixed charge of $5, i.e. it
costs $5 for the courier to arrive and $3 for every kilometre travelled to
deliver the documents.
An alternative definition of the gradient is:
The gradient is the rate of change of one variable with respect to
another.
Key Terms
gradient
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