Assuming That the Equations Define X and Y Implicitly as Differentiable

Multiple Choice

Assuming that the equations define x and y implicitly as differentiable functions x = f(t) , y = g(t) , find the slope of the curve x = f(t) , y = g(t) at the given value of t.
- $$2 \mathrm { tx } + 4 \mathrm { t } ^ { 2 } = 4,2 \mathrm { y } - \mathrm { t } ^ { 2 } - \mathrm { t } = 0 , \mathrm { t } = 1$$

A) $\frac { 3 } { 2 }$
B) $- \frac { 3 } { 8 }$
C) $- 6$
D) $\frac { 3 } { 8 }$