9x-4y=7

What is the slope of the line perpendicular to this line

What is the slope of a line parallel to this line

Well if you change it to standard form, you get y=9/4x+7/4. The important part of that is 9/4x. If a line is perpendicular, the slopes are opposite. The slope of a perpendicular line would be - 4/9x, don't forget the negative. And a parallel line has the same slope so any line with 9/4 is parallel but if the line has the same b value it is coinciding, not parallel and those aren't the same.

9x - 4y = 7

-4y = - 9x + 7

y = 9/4x - 7/4

slope of perpendicular line = - 4/9

slope of parallel line = 9/4