The equation of a line between two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]plugging the values given we have:
[tex]\begin{gathered} y-(-17)=\frac{-19-(-17)}{6-2}(x-2) \\ y+17=\frac{-19+17}{6-2}(x-2) \\ y+17=-\frac{2}{4}(x-2) \\ y+17=-\frac{1}{2}(x-2) \\ y+17=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1-17 \\ y=-\frac{1}{2}x-16 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{2}x-16[/tex]