Answer
$$y = - x - \frac{6}{5}$$
Work Step by Step
$$\eqalign{
& {x^2} = 5y;{\text{ }}\left( { - 2,\frac{4}{5}} \right) \cr
& {\text{Find }}\frac{{dy}}{{dx}}{\text{ using the implicit differentiation}} \cr
& \frac{d}{{dx}}\left[ {{x^2}} \right] = \frac{d}{{dx}}\left[ {5y} \right] \cr
& 2x = 5y\frac{{dy}}{{dx}} \cr
& \frac{{dy}}{{dx}} = \frac{{2x}}{{5y}} \cr
& {\text{Calculate the slope at the point }}\left( { - 2,\frac{4}{5}} \right) \cr
& \frac{{dy}}{{dx}} = \frac{{2\left( { - 2} \right)}}{{5\left( {4/5} \right)}} \cr
& m = - 1 \cr
& {\text{The equation of the tangent line at the given point is}} \cr
& y - {y_1} = m\left( {x - {x_1}} \right) \cr
& y - \frac{4}{5} = - \left( {x + 2} \right) \cr
& y - \frac{4}{5} = - x - 2 \cr
& y = - x - \frac{6}{5} \cr
& \cr
& {\text{Graph}} \cr} $$
