we have the equations
ay=4x+9 ------> equation 1
y=5x-7 -----> equation 2
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
that means
the product of their slopes is equal to -1
so
step 1
Find out the slope of equation N 2
y=5x-7
the slope is m=5
the slope of equation 1 must be equal to -1/5
(because 5*(-1/5)=-1)
step 2
Find out the slope of equation 1
ay=4x+9
isolate the variable y
y=(4/a)x+9/a
m=4/a
Equate 4/a to -1/5
4/a=-1/5
solve for a
20=-a
a=-20