The point $P(4 , 0.5 )$ lies on the curve $y = \frac{2}{x}$. If $Q$ is the point $(x, \frac{2}{x} )$, find the slope of the secant line $PQ$ for the following values of $x$.
If $x= 4.1$, the slope of $PQ$ is:
and if $x= 4.01$, the slope of $PQ$ is:
and if $x= 3.9$, the slope of $PQ$ is:
and if $x= 3.99$, the slope of $PQ$ is:
Based on the above results, guess the slope of the tangent line to the curve at $P(4 , 0.5 )$.