Question 1036056
<pre>
f(2) &#8804; f(3), f(4) &#8805; f(5), and f(6)=10

Since f(x) is a linear function, there exist numbers m
and b such that f(x) = mx+b

   2m+b &#8804; 3m+b,      and 4m+b &#8805; 5m+b,  and 6m+b = 10
                                              b = 10-6m

Substituting 10-6m for b

2m+10-6m &#8804; 3m+10-6m, and 4m+10-6m &#8805; 5m+10-6m

  -4m+10 &#8804; -3m+10,   and   -2m+10 &#8805; -m+b

      -m &#8804; 0,        and       -m &#8805; 0

       m &#8805; 0         and        m &#8804; 0

The only way both can be true is for slope m = 0 

Flat lines have slope 0, and ONLY flat lines
have slope 0.  Thus "f" is a flat line.

Edwin</pre>