Question

Please help, I keep messing up near the end:
Find the point on the line -6 x + 5 y - 6 =0 which is closest to the point ( 4, -3 ).

Answer 1

slope of -6 x + 5 y - 6 =0.............(a)
is 6/5
slope of a line perpendicular to the above is -5/6.
equn. of line with this slope passing thru (4,-3):
y --3 = (-5/6)(x - 4)
y + 3 = (-5/6)(x-4)...................(b)
solve (a) and (b) simultaneously will give you the required point.

Answer 2

Thank you for your help, I'm sorry for the trouble I was trying another method, what do you mean by solving them simultaneously

Answer 3

find values of x and y using elimination or substitution

b =
6y + 18 = -5x + 20
0r
5x + 6y - 2 = 0...........b
-6 x + 5 y - 6 =0.............(a)
multiply b by 6 and a by 5 and add to eliminate x

Answer 4

perfect, thank you very much!

Answer 5

yw