Say for all $m<1,$ and $a>1,$ you take all points $(a,b)$ and $(1/b,1/a)$ such that line $y=mx$ contains those points.
And for all $m>1,$ and $a>1,$ you take all points $(b,a)$ and $(1/a,1/b)$ such that line $y=mx$ contains those points.
For $m=1$ you take all points $c>0,$ $(c,c)$ and $(1/c,1/c)$ such that the line $y=mx$ contains that point.
And for all $m>1,$ and $a>1,$ you take all points $(b,a)$ and $(1/a,1/b)$ such that line $y=mx$ contains those points.
For $m=1$ you take all points $c>0,$ $(c,c)$ and $(1/c,1/c)$ such that the line $y=mx$ contains that point.