For what values of m, the relation
K= {(-1.5m +4, -23), (6m - 7,23)}
is not a function

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

and we can also include the negative of "m" or namely    

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )