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

Answer 1

Answer:

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

Step-by-step explanation:

$\textup{Given equation is: 4x + 36y = 80 }\\\textup{This can be written in the form of y = mx + a as follows}\\ 36y = -4x + 80 \\ \implies y = \frac{80}{36} - \frac{4}{36}x \\ \implies y = \frac{-1}{9}x + \frac{20}{9} \\\textup{This means that the slope of this line is m = \frac{-1}{9} }$

$\textup{Then the slope of the line perpendicular to this line would be \textbf{negative reciprocal of m}.}\\ i.e., \textup{Slope of the perpendicular line would be m_1 = \frac{-1}{\frac{-1}{9}} }\\ \implies m_1 = 9$

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

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