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

May 1, 2018

$\implies y = 3 x$

#### 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:

$y = \alpha x$

$6 = \alpha \left(2\right)$

$3 = \alpha$

So the relationship here is $y = 3 x$

May 1, 2018

$y = 3 x$

#### Explanation:

When two variables are directly proportional, it means that one is a constant multiple of the other. For example, in the equation $y = 16 x$, $y$ 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 $y = k x$, where $k$ is some constant multiple (a number).

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