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.
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
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