The given equation is
[tex]y=\frac{3}{8}x+6[/tex]We know that line v is perpendicular to u (the given equation).
The definition for perpendicularity in this case is
[tex]m_u\cdot m_v=-1[/tex]Additionally, from the given equation, we know that the slope of line u is 3/8. Using the perpendicularity definition, we have
[tex]\begin{gathered} \frac{3}{8}\cdot m_v=-1 \\ m_v=-\frac{8}{3} \end{gathered}[/tex]