The position of a particle moving in the $xy$-plane has the following parametric equations: $x(t) =\frac { 5 } { 3 t - 6 }$, $y(t) =\frac { 3 t } { 2 t + 6 }$

1. Determine the slope of the line tangent to the path of the particle when $t = 3$.

2. Write and interpret $\frac { d ^ { 2 } y } { d x ^ { 2 } }$.

   Hint (b):

   $\frac{d^2y}{dx^2}=\frac{d}{dx}\Big(\frac{dy}{dx}\Big)=\frac{d}{dx}\Big(\frac{y^\prime(t)}{x^\prime(t)}\Big)=\frac{dt}{dx}\cdot\frac{d}{dt}\Big(\frac{y^\prime(t)}{x^\prime(t)}\Big)=\frac{\frac{d}{dt}\Big(\frac{y^\prime(t)}{x^\prime(t)}\Big)}{\frac{dx}{dt}}$