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)`.

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

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

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