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

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) (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) (Show Source): You can put this solution on YOUR website!
Because the curve has a tangent line of at , this means that the curve intersects the line at 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 into to get .

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