find an equation of the tangent line to the curve at the given point

(hyperbola)

$\displaystyle \frac{x^2}{16}-\frac{y^2}{9} = 1\ \left(-5,\frac{9}{4}\right)$

using the quotient rule $\displaystyle \frac{vu'-uv'}{v^2}$

$\displaystyle \frac{16(2x)-x^2(0)}{16^2}-\frac{9(2yy')-y^2(0)}{9^2}

\Rightarrow

\frac{x}{8}-\frac{2yy'}{9}

\Rightarrow

y'=\frac{9x}{16y}

$

so $\displaystyle m=\frac{9(-5)}{16(\frac{9}{4})}\Rightarrow-\frac{5}{4}$

the given answer is $\displaystyle y=-\frac{5}{4}x-4$

but did not see how this was derived (providing my y' was correct)