It can be proved using the method of inverse variation.
What is inverse variation?
In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.
Given,
(x₁, y₁) and (x₂, y₂) are values from an inverse variation.
inverse function of x and y will be -
y1 = k. 1 / x1
k = y1 / x1 ....(1)
y2 = k. 1 / x2
k = y2 / x2 ....(2)
from (1) , (2)
we can say that,
y1 / x1 = y2 / x2
⇒ y2 / y1 = x1 / x2
Hence proved.
To learn more about inverse variation from given link
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