**Direct variation may be understood by scenarios from our daily life.**

**For example: **An employee who works for hourly wages may be paid according to the number of hours he worked. The two quantities *x* (the number of hours worked) and *y* (the amount paid) are related in such a way that when *x* changes, *y* changes proportionately such that the ratio remains a constant.

I.e., *y* **varies directly** with *x*. Let us represent the constant by *k*, i.e.

or *y = kx* ( where *k* ≠ 0)

If *y* varies directly as *x*, this relation is written as *y* ∝ *x *and read as *y* varies as *x*. The sign “ ∝ ” is read “varies as” and is called the **sign of variation**.

*Example:*

If *y* varies directly as *x* and given *y* = 9 when *x* = 5, find:

- the equation connecting
*x*and*y* - the value of
*y*when*x*= 15 - the value of
*x*when*y*= 6

*Solution:*

a) y x i.e. y = kx where k is a constant

Substitute x = 5 and y = 9 into the equation:

y = x

b) Substitute x = 15 into the equation

y = = 27

c) Substitute y = 6 into the equation