#4201. Direct Variation

Mathematics, level: Senior
Posted Thu Jun 26 05:12:30 PDT 2008 by Guido Feliz, Jr (Guido Feliz, Jr).
DOE, NYC
Materials Required: Pencil and paper
Activity Time: 15 minutes
Concepts Taught: Idea Behind Constant Ratio

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

The equation above 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 where it is.

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

Final answer: S = kh

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