Question

(2,-5) perpendicular to -7x+8y=-9

Answer 1

-7x + 8y = -9
         8y = 7x - 9
           y = 7/8x - 9/8 

so line -7x+8y=-9 has slope = 7/8

perpendicular lines, slope will be opposite and reciprocal
so new line has slope = -8/7

passing thru (2,-5) 
y = mx + b
-5 = -8/7(2) + b
-5 = -16/7 + b
b = -5 + 16/7
b = -35/7 + 16/7
b = -19/7

equation
y = -8/7x - 19/7

hope it helps