Question

Find the point on the line 6x+y=9 that is closest to the point (8−9).

Answer 1

the closest point on the line 6x+y=9 is the point of intersection of the line and the line perpendicular to it passing through the point (8,-9).
any line perpendicular to 6x+y=9 is of the form x-6y=c
in this particular case the perpendicular line passes through the point (8,-9)
so the equation of the perpendicular line is x-6y=62
now all you have to do is find out the point of intersection between 6x+y=9 and x-6y=62
from equation i,
36x+6y=54
from equation ii,
x-6y=62
adding those two,
37x=116
or, x=116/37
so, y=9-6*116/37

Answer 2

Thanks :), I got it, although you make it look easier lol