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Sagot :
To find the perpendicular line, first, let's rewrite this line in slope-intercept form. The slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Rewritting our line equation on this form, we have
[tex]\begin{gathered} 5x-8y=-3 \\ -8y=-5x-3 \\ 8y=5x+3 \\ y=\frac{5}{8}x+\frac{3}{8} \end{gathered}[/tex]The slope of the perpendicular line is minus the inverse of the slope of our line.
[tex]m_{\perp}=-(\frac{5}{8})^{-1}=-\frac{8}{5}[/tex]Then, this means the perpendicular line have the form
[tex]y=-\frac{8}{5}x+b[/tex]To find the coefficient b, we can evaluate the point we know that belongs to this line.
[tex]\begin{gathered} (3)=-\frac{8}{5}(-5)+b \\ 3=8+b \\ b=3-8 \\ b=-5 \end{gathered}[/tex]Our perpendicular line is
[tex]y=-\frac{8}{5}x-5[/tex]
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