Question

Consider the line -9x-4y=-2.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?Would the perpendicular slope be -4/9 and the parallel line be 9/4?

Answer 1

$-9x-4y=-2$

first we solve the equation for y

$\begin{gathered} -4y=-2+9x \\ \\ y=\frac{-2+9x}{-4} \\ \\ y=\frac{1}{2}-\frac{9}{4}x \end{gathered}$

on this line the slope is the coefficient of x, so the number that accompanies the variable x

the slope is

$-\frac{9}{4}$

for a line to be perpendicular to it, it must have the inverted fraction and the opposite sign to the original slope

then

$-\frac{9}{4}\longrightarrow\frac{4}{9}$

the slope of the perpedicular line is 4/9

and the slope of a parallel line must be the same slope, so

$-\frac{9}{4}$