Answer
$$y = m\left( {x - 4} \right) - 2$$
Work Step by Step
$$\eqalign{
& {\text{We know the slope }}m{\text{ and the point }}\left( {4, - 2} \right) \cr
& {\text{use the point - slope form of equation of a line }}y - {y_1} = m\left( {x - {x_1}} \right) \cr
& {\text{from the point }}\left( {4, - 2} \right){\text{ we obtain }}{x_1} = 4{\text{ and }}{y_1} = - 2 \cr
& {\text{then}} \cr
& y - {y_1} = m\left( {x - {x_1}} \right) \cr
& y - \left( { - 2} \right) = m\left( {x - 4} \right) \cr
& {\text{simplifying}} \cr
& y + 2 = m\left( {x - 4} \right) \cr
& y = m\left( {x - 4} \right) - 2 \cr} $$
