Question

Find an equation to the line perpendicular to 4x + 36y =80 an goes through the point (3,6) write answer in form y= Mx+b

Y= ?

Answer 1

`\textbf{y = 9x + 21 }\\`

Explanation:

`\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 = (80)/(36) - (4)/(36)x $\\$ \implies y = (-1)/(9)x + (20)/(9) $\\\textup{This means that the slope of this line is $m = (-1)/(9)$}\\`

`\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 $m_1 = (-1)/((-1)/(9))$}\\$\implies m_1 = 9$\\`

`\textup{The perpendicular line passes through the point $(3,6)$}\\\textup{Using the \textbf{point-slope formula}, we get:}\\`

`$$ y - y_1 = m(x - x_1) $$$ \implies y - 6 = 9(x - 3) $\\\textup{After solving this reduces to $y = 9x + 21$ }`