Challenge Level

Jiwon Jung noticed:

The lines that are reflections have the same absolute value of their x coefficient and the constant.

Well noticed. Ellie from Chiswick matched up the reflections, and explained why they work:

A straight line is $y=ax+b$, where $a$ and $b$ are constants,
and can be positive or negative.

If you reflect in the $x$ axis, then all the $y$ values become
$-y$, so the line becomes $-y=ax+b$, which we write
$y=-ax-b$.

If we reflect in the $y$ axis, then the $x$ values become
$-x$, and the line becomes $y=a(-x)+b$, which is $y=-ax+b$.

Now we can match the lines.

Then I looked at doing both reflections.

First, I tried reflect in $x$, then $y$, using the rules
above.

$y=ax+b$ reflected in $x$ is $y=-ax-b$, then reflected in $y$
becomes $y=ax-b$

Now try the other way around.

$y=ax+b$ reflected in $y$ is $y=-ax+b$, then reflected in $x$
becomes $y=ax-b$

So it doesn't matter which way round you do the reflections.
The twice reflected graph has the same gradient as the original,
but translated down so it crosses the $y$ axis at the opposite
place.