Determine the slope of the line which goes through the point (2, -5)
and is perpendicular to the line determined by 5x-4y=9.

Hi haylo!!


Use the following property:

"Two non vertical lines are perpendicular if and only if their slopes
m1 and m2 are negative reciprocals, in other words m1*m2 = -1 or m2 =
-1/m1 ."


We have the line determined by 5x-4y = 9, it is equivalent to:

y = 5/4*x - 9/4 ;

Then m1 = 5/4 and m2 = -1/m1 = -1/(5/4) = -4/5 .


It does not matter if a perpendicular line to the line determined by
5x-4y=9 goes through point A or B, its slope will be -4/5.

So the answer to this problem is:
The slope of the line which goes through the point (2, -5)
and is perpendicular to the line determined by 5x-4y=9 is -4/5. 


Hope this helps. If you need a clarification, please do not hesitate
to request for it before rate this answer.

Regards.
livioflores-ga