the equation of a perpendicular line to another, is the negative reciprocal of the other, or each other, so hmm let's see what's the slope of 3x -5y = -4 then
[tex]\bf 3x-5y=-4\implies 3x+4=5y\implies \cfrac{3x+4}{5}=y\implies \stackrel{slope}{\cfrac{3}{5}}x+\stackrel{}{\cfrac{4}{5}}=y[/tex]
so, what is the slope of a line perpendicular to that one then?
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{3}{5}\\\\
slope=\cfrac{3}{{{ 5}}}\qquad negative\implies -\cfrac{3}{{{5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{3}[/tex]
