Answer :
[tex]\bf 4x-8y+3=0\implies -8y=-4x-3\implies y=\cfrac{-4x-3}{-8}
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y=\cfrac{-4}{-8}x+\cfrac{3}{8}\implies y=\cfrac{1}{2}x+\cfrac{3}{8}\\\\
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\textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
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[tex]\bf -------------------------------\\\\ \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2} \\\\\\ slope=\cfrac{1}{2}\qquad negative\implies -\cfrac{1}{2}\qquad reciprocal\implies -\cfrac{2}{1}\implies -2[/tex]
[tex]\bf -------------------------------\\\\ \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2} \\\\\\ slope=\cfrac{1}{2}\qquad negative\implies -\cfrac{1}{2}\qquad reciprocal\implies -\cfrac{2}{1}\implies -2[/tex]