What do you call the number k, that you must multiply with x, in order to get y?

Question

In the equation:

$$y = kx$$

The coefficient or constant $k$, represents how many multiples of $x$ are required to equal $y$.

What is the term for $k$, in that it represents the quotient of $y/x$?

If we were looking at $y:x$, we would call that the ratio of $y$ and $x$.

Similarly if we had $y/x$, we would call that the _____ of $y$ and $x$.

I tried to Google this term for 10 minutes before giving up in the floods of children's math websites and colloquial english usage of the words "fraction", "ratio", etc.

Answer 1

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be linear function, i.e. \begin{align} f(x) = kx, \end{align} for some $k\in\mathbb{R}$. $k$ is sometimes called the slope of $f$.

Answer 2

In this context where $$ y=kx, $$ we say $y$ is proportional to $x$ with a coefficient of proportionality equal to $k$ (see link for other widely used names). In some cases the value of $k$ is not important and we simple write $$ y\propto x, $$ which simply reads "$y$ is proportional to $x$".