Consider the graph of the function $f(x)=-x^2+6.$

$($a$)$ Find the equation of the secant line joining the points $(-1,5)$ and $(2,2).($Enter your answer in terms of $x$ and $y.)$

$($b$)$ Use the mean value theorem to determine a point $c$ in the interval $(-1,2)$ such that the tangent line at $c$ is parallel to the secant line. $c=$

$($c$)$ Find the equation of the tangent line through $c.($Enter your answer in terms of $x$ and $y.)$