Answer :
Two lines are perpendicular if and only if their slopes fulfil:
[tex]m_1m_2=-1[/tex]All of the equations are given in the form:
[tex]y=mx+b[/tex]Then, the equation
[tex]y=-\frac{5}{3}x-6[/tex]has slope:
[tex]m_1=-\frac{5}{3}[/tex]Plugging this in the perpendicular relation we have that:
[tex]\begin{gathered} -\frac{5}{3}m_2=-1 \\ m_2=\frac{-1}{-\frac{5}{3}} \\ m_2=\frac{3}{5} \end{gathered}[/tex]this means that any perpendicular line to the one given has to have slope 3/5.
From the options given we notice that the only line that has this slope is:
[tex]y=\frac{3}{5}x-10[/tex]Therefore, the perpendicular line is the last option.