What is the equation of the line perpendicular to 2x + 5y = 20 that contains the point (10, −4)?

Perpendicular means a line that is opposite and reciprocal to the slope you have now 

1) first solve for y

5y= -(2x) + 20 
y= -(2/5)x + 4 

so the slope is -2/5 so perpendicular is  m= 5/2 

so now use point slope 

y-y1=m(x-x1)

m=5/2 and point is (10,-4) 

plug and chug

y+4 = (5/2) (x-10 )

y= 5/2x - 25 - 4
y=5/2x - 29

hope i didnt make an adding error 
but thats how you do it.

hope that helps