Proportion and Inverse Proportion

## Proportion and Inverse Proportion

If two variables are in Direct Proportion, then as the value of one variable increases, the other variable also increases.

The relationship is shown as y prop x.

If two variables are in Inverse Proportion, then as one variable increases, the other variable falls.

The relationship is shown as y prop frac(1)(x).

## Example 1

Two variables, x and  y, are known to be in direct proportion. The value of x is doubled. What happens to the value of y?

Use an example to show it.

As the two values are in direct proportion, then one value will increase at the same rate as the other.

y prop kx

y = kx

Say y=3 and x=9 then 3=9k, k=frac(1)(3)

if x doubles to 18 then

y = kx

y = frac(1)(3)(18)

y = 6, which has doubled.

Answer: It will double

## Example 2

Two variables, x, are known to be in inverse proportion where y = frac(1)(x). What happens to the value of y, if the value of x is halved?

As the two variables are in inverse proportion, then halving one will double the other, and vice versa.

Use an example.

Say y = 2 and x=8

y prop frac(1)(x)

y = frac(k)(x)

2 = frac(k)(8)

k = 16

Halve x to 4

y = frac(k)(x)

y = frac((16))((4))

y = 4 (it has doubled)

Answer: It will double