The point $P(4,-4)$ lies on the curve $y=\frac{4}{3-x}.$

$($a$)$ If $Q$ is the point $(x,\frac{4}{3-x}),$ find the slope of the secant line $PQ($correct to six decimal places$)$ for the following values of $x.$

$($i$)3\mathrm{.}9$

$m_{PQ}=$