Two variables are in direct proportion to one another if they are always in the same ratio.

If two variables x and y are vary in such a way that their ratio x/y is a constant(k). Then x and y are said to vary directly or in direct variation "k" is called the constant of variation.

\ If variables x and y are directly then x/y = k or x=ky.

This is denoted by x¥y.

Example:
y¥x, and constant of variation is 6. Find y, when x=3, find x, when y=24.

Solution:
Since y¥x, we have y = kx
But k = 6 Þ y = 6x
If x = 3 Þ y = 6*3 = 18
If y = 25 Þ 25 = 3x Þ x = 25/3.

Example:
If 4 bottles of milk cost $2, how many bottles can you buy for $8? Solution:
You can write this in proportion as
4:2 :: x:8
or
4/2 = x/8
Cross multiplying we get
2x = 32
x = 16
Answer: 16 bottles

Directions: Solve the following problems. Also write atleast 10 examples of your own.