Find $d y / d x$ Implicitly and Explicitly(the Explicit Functions Are Shown on the Graph)

Multiple Choice

Find $d y / d x$ implicitly and explicitly(the explicit functions are shown on the graph) and show that the results are equivalent. Use the graph to estimate the slope of the tangent line at the labeled point. Then verify your result analytically by evaluating $d y / d x$ at the point.

A) $\frac { 1 } { 2 y } , - \frac { 1 } { 2 }$
B) $- \frac { 1 } { 2 y } , \frac { 1 } { 2 }$
C) $- \frac { 1 } { 2 y } , - \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 y } , \frac { 1 } { 2 }$
E) $\frac { 1 } { 2 } , - \frac { 1 } { 2 }$