I am currently studying graphs of modular equations and was wondering if there exists a modular equation for any 2 perpendicular lines and if this is the case what method would you use to find this modulus equation if you are given the equation of both perpendicular lines.
For example:
the modulus equation $|y|=|x-1|$ could be graphed as the intersection of the two lines $y=x-1$ ad $y=-x+1$.
now if we work backward, would that always work?
For example:
For the two perpendicular lines $y=\frac{x}{2}$ and $y=-2x$ does there exist a modulus equation and how would you go on to find what it is.
Also feel free to edit or add tags.
$\left|3y+x\right|=\left|3x-y\right|$ gives your equations.