Is being directly negatively proportional same as being inversely proportional? If I have the proportionality
$$x\propto-y$$
It suggests that x increases with $-y$ and since there's a negative symbol present it would mean that the lower the value of $y$ the higher the value of $x$...so does this still qualify as directly proportional?
It does seem to be different from $x\propto\frac{1}y$ so I guess it's not inversely proportional?
The direct relation of $y$ with $x$ sounds wrong to be called directly proportional, so what exactly is a negative proportionality called if not being the same as inversely proportional?
Thanks.
 A: The short answer is that they are not the same. If something is negatively proportional, its graph may be a  line going from upper left to lower right. There is a negative constant involved $\quad -\infty\lt c \lt 0\quad$ so the angle with the x-axis  may be
$\quad \large{\dfrac{\pi}{2}
\lt\alpha\lt\pi}.\quad$ If something is inversely proportional, sign is irrelevant and its graph may be one, two, or four ski slopes with both horizontal and vertical  asymptotes.
A: *

*Actually, $\;x=5y\;$ and $\;x=-5y\;$ can equally be written as
$$x\propto y,$$ which is defined as $$x=ky \:\:\:\text{for}\; k\ne0;$$
so, the negative sign in $\:\:x\propto-y\:\:$ is in fact redundant.
This reinforces the fact that ‘negative proportionality’ is a
type of direct proportionality.
To disambiguate the former from negative inverse proportionality,
we might say that $x$ is directly proportional but opposite in sign
to $y.$


*

$$x\propto-y$$
The direct relation of y with x sounds wrong to be called directly proportional

You're saying that

*

*$x$ is directly proportional to $-y,$
rather than saying that

*

*$x$ is directly proportional to $y,$
so how is there any anomaly? The former is analogous to using the
word “add” in the instruction

*

*add $-3$ to $7.$



*To be clear, $$x\propto-y$$ and inverse proportionality
$$x\propto\frac1y$$ are not equivalent, because as $y$ becomes large,
$x$ approaches zero in the latter but not the former.
