Guido Feliz Jr.
Math Lesson: Direct Variation



By Guido Feliz, Jr

(c) 2008



When two variable quantities have a constant ratio,
their relationship is called a direct variation.
It is said that one variable "varies directly" as the other variable.

The constant ratio is called the constant of variation.

The formula for direct variation normally used is y = kx,
where k is the constant of variation.

The equation is read: "y varies directly as x"

To solve for k, divide both sides of the equation by x. Doing so, we get

k = y/x, where y = numerator; x = denominator.



In a direct variation problem, the two variables
change at the same time. In other words, if one increases, so does the other.



Example:

The weekly salary a man earns, S, varies directly as the number of hours, h, which he works. Express this relation as a formula.



Solution:



The formula for direct variation is y = kx,
where k is the constant of variation.
The equation is read: "y varies directly as x."



Since S varies directly as h in the question, let y = S and x = h in the equation y = kx. In other words, replace y with S and x with h. Leave k alone.



Doing so, we can then write the relation between S and h as a formula

this way: S = kh.



Final answer: S = kh



NOTE: To find k in the equation S = kh, simply isolate k (place k all alone on one side of the equation) by dividing both sides by h. It then looks like this: S/h = k.
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