Question

Y is directly proportional with x. Write an equation that shows the relationship if x = 2 and y = 6?

Answer 1

`=>y = 3x`

Explanation:

Direct proportionality is defined as:

`y = alpha x`

where `alpha` is some constant that defines the proportionality.

Given `x = 2` and `y = 6`, we find:

`y = alpha x`

`6 = alpha (2)`

`3 = alpha`

So the relationship here is `y = 3x`

Answer 2

`y = 3x`

Explanation:

When two variables are directly proportional, it means that one is a constant multiple of the other. For example, in the equation `y = 16x`, `y` is directly proportional to `x`, because `y` is just some constant multiple of `x`. (In this case, the constant multiple is 16.)

The equation `y = x^2` does not represent a directly proportional relationship, because `y` is not some constant multiple of `x`.

To the problem at hand -- we are given that `y` and `x` are directly proportional. This means `y` is a constant multiple of `x`. This can be written as `y = kx`, where `k` is some constant multiple (a number).

We have the equation `y = kx` and we are also told that `x = 2` and `y = 6`. We can directly plug these in to determine the value of `k`. `y = kx -> 6 = 2k -> k = 3`. Thus, our relationship is given by the equation `y = 3x`. This is our final answer.