Answer:
[tex]\textbf{y = 9x + 21 }\\[/tex]
Step-by-step explanation:
[tex]\textup{Given equation is: $4x + 36y = 80 $}\\\textup{This can be written in the form of $y = mx + a$ as follows}\\$ 36y = -4x + 80 $\\$ \implies y = \frac{80}{36} - \frac{4}{36}x $\\$ \implies y = \frac{-1}{9}x + \frac{20}{9} $\\\textup{This means that the slope of this line is $m = \frac{-1}{9}$}\\[/tex]
[tex]\textup{Then the slope of the line perpendicular to this line would be \textbf{negative reciprocal of m}.}\\$i.e.,$ \textup{Slope of the perpendicular line would be $m_1 = \frac{-1}{\frac{-1}{9}}$}\\$\implies m_1 = 9$\\[/tex]
[tex]\textup{The perpendicular line passes through the point $(3,6)$}\\\textup{Using the \textbf{point-slope formula}, we get:}\\[/tex]
[tex]$ y - y_1 = m(x - x_1) $$ \implies y - 6 = 9(x - 3) $\\\textup{After solving this reduces to $y = 9x + 21$ }[/tex]
