Find the point on the line -3 x + y + 4 =0 which is closest to the point ( -5, 0 ).
distance=sqrt((x+5)^2+ (y)^2)
but y=3x-4
distance= sqrt((x+5)^2 + (3x-4)^2)
I think it will be easier to do this..
distance^2=((x+5)^2+(3x-4)^2) then take the deravative
2distane*ddistan/dx=0=2(x+5)+2(3x-4)*3
or x+5=-9x+12 check that, then solve for x, then solve for y on the line
check my work, I did it all in my head and on the keyboard.