Question 1184566

It is rather strange that two tutors make the same calculational mistake:  One made the error at the highlighted parts -- 


{{{matrix(3,3, (2 - - 2)/green((k - 5)), "=", - 16/21, 4/red((k - 2)), "=", - 16/21, 1/red((k - 2)), "=", - 4/21)}}}.


That said, a correct solution is as follows:


Since the line is supposed to be parallel, it must be of the form


{{{16x + 21 y = C}}}, for some constant C.


Since (5,-2) is on this line, ===> {{{16*5 + 21*-2 = C}}}   ===> C = 38.


===> {{{16x + 21 y = 38}}}  is the desired parallel line.


Since (k,2) is also on this line, ===> {{{16*k + 21*2 = 38}}}   ===> {{{highlight(k = -1/4)}}}.