Given data:
The given equation is 10x+6y= -84.
The given equation can be written as,
[tex]\begin{gathered} 6y=-10x-84 \\ y=-\frac{10}{6}x-\frac{84}{6} \\ =-\frac{5}{3}x-14 \end{gathered}[/tex]The standard equation of the line is,
[tex]y=mx+c[/tex]Compare both the equations.
[tex]m=-\frac{5}{3}[/tex]The expression for the slope perpendicular to the given line is,
[tex]\begin{gathered} m^{\prime}=-\frac{1}{m} \\ m^{\prime}=-\frac{1}{(-\frac{5}{3})} \\ =\frac{3}{5} \end{gathered}[/tex]Thus, the slope of the line perpendicular to the given line is 3/5.
