Answer
$m_{a}=-\frac{1}{2}$
$m_{b}= -1$
Work Step by Step
The slope of the tangent line at a given point is equivalent to the derivative of the line evaluated at that point.
$a.) y = x^{-\frac{1}{2}}$
Use the power rule to differentiate:
$y' = -\frac{1}{2}x^{-\frac{3}{2}}$
Now since the point we are evaluating is at one, 1 to any exponent is itself. Leaving us with $-\frac{1}{2}$ as the slope of the tangent line at $(1,1)$.
$y' = -\frac{1}{2}1^{-\frac{3}{2}}$
$y' = -\frac{1}{2}$
Now do the same thing with the other function.
$b.) y = x^{-1}$
$y' = -1x^{-2}$
$y' = -1 (1)^{-2}$
$y' = -1$
