Find the point on the line 6x+y=9 that is closest to the point (-3,1).

Question

anonymous · Answer

6x + y = 9
y = -6x + 9
slope is -6

perpendicular would have slope 1/6
(y - 1) = (1/6) (x + 3)
y - 1 = (1/6) x + (1/2)
multiplying both sides by 6
6y - 6 = x + 3
x - 6y = -9 _______1


From above we know given equation is y = -6x + 9
substitute this equation in 1 
x - 6(-6x + 9) = -9
x + 36x - 54 = -9
37 x = 45
x = 45/37
y = -6(45/37) + 9
y = -270/37 + (333/37)
y = 63/37

point is (45/37, 63/37)

anonymous · Answer

@ASAAD123 http://answers.yahoo.com/question/index?qid=20081106202035AAlEt5X The above solution is algebraic, but since this is a calculus section lets explore calculus type solutions: |dw:1353354005150:dw|