$[-/14\mathrm{.}28$ Points$]$

DETAILS

The point $P(5,-3)$ lies on the curve $y=\frac{3}{4-x}.$

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

$(1)4\mathrm{.}9$

$m_{PQ}=$

$$

$($II$)4\mathrm{.}99$

$m_{PQ}=$

$($iii$)4\mathrm{.}999$

$m_{}=$

$($iv$)4\mathrm{.}9999$

$m_m=$

$($v$)5\mathrm{.}1$

$m_{}=$

$$

$($vi$)5\mathrm{.}01$

$m_{AQ}=$

$($vii$)5\mathrm{.}001$