by definition a function has no X-repeats, or namely the set K must not have any x-values for any of the coordinate pairs repeated, so the x-values must be unique for each pair, now if it ever happens that for some reason two values end up being the same or equal, then holy smokes, we no longer have a function, hmmm well, when will that happen? that can happen if -1.5m + 4 = 6m - 7
[tex]-1.5m+4=6m-7\implies 4=7.5m-7\implies 11=7.5m\implies 11=\cfrac{15m}{2}\\\\\\22=15m\implies \cfrac{22}{15}=m\implies 1\frac{7}{15}=m[/tex]
and we can also include the negative of "m" or namely [tex]\pm1\frac{7}{15}=m[/tex]
