We have to find the slope of the line that passes thorugh points (19/2, -8/3) and (-7/2, -1/15).
We can find the slope m as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-\frac{1}{15}-(-\frac{8}{3})}{-\frac{7}{2}-\frac{19}{2}} \\ \\ m=\frac{-\frac{1}{15}+\frac{8}{3}\cdot\frac{5}{5}}{\frac{-7-19}{2}} \\ \\ m=\frac{-\frac{1}{15}+\frac{40}{15}}{\frac{-26}{2}} \\ \\ m=-\frac{2}{26}(\frac{39}{15}) \\ \\ m=-\frac{1}{13}(\frac{13\cdot3}{5\cdot3}) \\ \\ m=-\frac{1}{5} \end{gathered}[/tex]
We can check the result with a graph as:
Answer: the slope is m = -1/5.
