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=(-2+9x)/(-4) \\ \\ y=(1)/(2)-(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

`-(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

`-(9)/(4)\longrightarrow(4)/(9)`

the slope of the perpedicular line is 4/9

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

`-(9)/(4)`