9514 1404 393
Answer:
y = -x/16 +1
Step-by-step explanation:
The slope is at any point x is ...
y' = -4/x^2
so, at x=8, the slope is ...
m = -4/8^2 = -4/64 = -1/16
The point-slope form of the equation of the line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Then the line with slope -1/16 through point (8, 1/2) is ...
y - 1/2 = -1/16(x -8)
y = -1/16x +1/2 + 1/2 . . . . . eliminate parentheses, add 1/2
y = -1/16x +1 . . . . . equation of the tangent line
