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