Answer:
(a) -1/25
(b) y = -1/25x +2/5
Step-by-step explanation:
You want the slope and tangent line equation for the curve y = 1/x at point P(5, 1/5).
(a) Slope
The slope is the derivative of the function at the given point:
y = 1/x = x^(-1)
y' = (-1)x^(-1-1) = -1/x²
At x=5, the slope is ...
m = -1/5² = -1/25
(b) Equation
The equation of the tangent line is conveniently written using slope-intercept form:
y -k = m(x -h) . . . . . . . . equation for line with slope m at point (h, k)
y -1/5 = -1/25(x -5) . . . . equation for line with slope -1/25 at point (5, 1/5)
Rearranging, we have the slope-intercept form ...
y = -1/25x +2/5
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