The slope-intercept form of the line is given by:
[tex]\begin{gathered} y=mx+b \\ m=slope \\ b=y-intercept \end{gathered}[/tex]for the line:
[tex]y=\frac{2}{5}x-8[/tex][tex]m=\frac{2}{5}[/tex]If two lines are perpendicular, then:
[tex]\begin{gathered} m1\times m2=-1 \\ so\colon \\ \frac{2}{5}\times m2=-1 \\ m2=-\frac{1}{\frac{2}{5}} \\ m2=-\frac{5}{2} \end{gathered}[/tex]Therefore, the equation that represents the line perpendicular to the line y = 2/5x - 8 is:
[tex]y=-\frac{5}{2}x+9[/tex]