SOLUTION: The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the value of k? (A) -3 (B) -1 (C) 1 (D) 3 (E) 4

Algebra ->  Test -> SOLUTION: The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the value of k? (A) -3 (B) -1 (C) 1 (D) 3 (E) 4      Log On


   

Question 261485: The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the value of k?
(A) -3
(B) -1
(C) 1
(D) 3
(E) 4
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Just plug y=2 and x=-2 and solve for k
k=3

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Because the curve y=%28kx%2B8%29%2F%28k%2Bx%29 has a tangent line of y=x%2B4 at x=-2, this means that the curve intersects the line at x=-2 and they intersect at the same 'y' value. In other words, the curve and the line intersect at the point (-2, y). Because these y values are the same, we can plug y=x%2B4 into y=%28kx%2B8%29%2F%28k%2Bx%29 to get x%2B4=%28kx%2B8%29%2F%28k%2Bx%29.


Now plug in x=-2 (since they intersect at x=-2) to get -2%2B4=%28-2k%2B8%29%2F%28k-2%29 and simplify to get 2=%28-2k%2B8%29%2F%28k-2%29. From here, it's just a simple matter of solving for k which I'll let you do.