Given two points on a line, we can find its slope using the following formula
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2)\to\text{ points on the line} \\ \Rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} (x_1,y_1)=(5,-7),(x_2,y_2)=(2,9) \\ \Rightarrow m=\frac{9-(-7)}{2-5}=\frac{9+7}{-3}=\frac{16}{-3}=-\frac{16}{3} \\ \Rightarrow m=-\frac{16}{3} \end{gathered}[/tex]Therefore, the slope is equal to -16/3.