The point $P(7,-4)$ lies on the curve $y=\frac{4}{6-x}$

$($a$)$ If $Q$ is the point $(x,\frac{4}{6-x}),$ find the slope of the secant line $PQ($correct to six decimal places$)$ for the following values of $x.$

$0\mathrm{.}6\mathrm{.}9$

$m_{FO}=$ Great werel

$($i$)6\mathrm{.}99$

$m_{10}=$ Perfect

$($ii$)6\mathrm{.}999$

$m_{f0}=$

$($iv$)6\mathrm{.}9999$

$m_{PO}=$ Good jobt

$($v$)7\mathrm{.}1$

$m_{PQ}=$

$$ x

$($vi$)7\mathrm{.}01$

$m_{PO}=$

$x=$

$($vi$)7\mathrm{.}001$

$m_{PQ}=$

$($vii$)7\mathrm{.}0001$

$m_{pq}=,x$

$($b$)$ Using the results of part $($a$),$ quess the value of the slope of the tangent, line to the curve at $A(7,-4).$

$m=$ Amaring jobt

$($c$)$ Using the slope from part $($b$),$ find an equation of the tangent line to the curve at $PC,-4).$

$$ templessive work.