Direct Variation Formula
As per the direct variation formula, direct variation exists between any two variables when one quantity is directly dependent on the other i.e. if one quantity increases with respect to the other quantity and vice versa. It is the relationship between two variables where one of the variables is a constant multiple of the other. Since the two variables are directly related to each other it is also termed as directly proportional. Thus, the ratio of these two variables is always a constant number. Let's look into the mathematical representation of the direct variation formula.
What is the Direct Variation Formula?
Let's consider two variables x and y. If the quantity y is directly varying with respect to the quantity x i.e, y ∝ x, then the direct variation formula is given by,
y = kx
where,
k is the constant of proportionality.
Since the variables y and x are in a directly proportional relationship, their ratio is always a constant number i.e, k.
Thus, y/x = k
Let's say \(y_1\) directly varies with \(x_1\) and \(y_2\) directly varies with \(x_2\) then, the direct variation formula is given by,
\(\dfrac{y_1}{ x_1} = \dfrac{y_2}{x_2}\)
Below is the graph is shown for the direct variation relationship between x and y.
Let's move on to the solved examples section and explore problems on direct variation formula
Solved Examples Using Direct Variation Formula

Example1: Let us assume that y varies directly with x, and y = 30 when x = 6. What is the value of y when x = 100?
Solution:
Given: \(y_1\)_{ }= 30, \(x_1\) = 6, \(x_2\) = 100, \(y_2\) = ?
Using direct variation formula,
\(y_1 / x_1 = y_2 / x_2\)
⇒ 30/6 = \(y_2\) / 100
⇒ 5 = \(y_2\) / 100
⇒ \(y_2\) = 500
Answer: Thus, the value of y when x = 100 is 500.

Example 2: The quantity of Iron boxes made is directly proportional to the number of iron blocks. The number of iron blocks needed for 40 boxes is 160. How many iron blocks are needed for a box?
Solution:
In the given problem,
Number of iron blocks needed for 40 boxes = y = 160
Number of boxes = x = 40
Number of iron blocks needed for a box = k
The direct variation formula is,
y = kx
⇒160 = k × 40
⇒k = 160/40
⇒k = 4
Answer: Thus, the number of iron blocks needed for a box is 4.