Introduction
- A gradient describes how much y changes relative to a change in x.
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For example, we can define a line as starting at (0, 0) and ending at (10, 25):
- Instead of giving explicit start and end points for the line we can describe it by how much y changes relative to x.
- In the line above, a change of 10 in x produces a change of 25 in y.
- The gradient is defined as the change in y divided by the change in x.
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If we use Δ to denote 'change' then the formula for the gradient (g) of a line is:
LaTeX:g = \frac{\Delta y}{\Delta x}
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In the line above, the gradient is:
Finding the change in x and y
- In our above example, our first coordinate was (9, 0). This made it easy to calculate how much x and y changed.
- However when both coordinates are non-zero, it gets a bit more complicated.
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For example, calculate the gradient of the line between (1, 2) and (7, 10)
- To find how much x and y change, we need to subtract the first coordinate from the second
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We can use this in our equation to find the gradient of a line:
Special Cases
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There are two special cases to look out for when calculating the gradient of a line:
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When the line is horizontal
- There will be no change in y
- The gradient is 0
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When the line is vertical
- There will be no change in x
- The gradient is infinity
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When the line is horizontal
Code
import math
def findGradient(p1, p2):
deltaY = p2[1] = p1[1]
deltaX = p2[0] - p1[0]
if deltaX == 0:
return math.inf
else:
return deltaY / deltaX
gradient = findGradient([1, 2], [7, 10])
print(gradient) # prints 0.3333333333333333