i) one of the forms that we can write the equation of a line is
y=mx+k
where m is the slope of the line.
ii)
given lines y=mx+k and y=nx+t, which are perpendicular to each other.
Then, m*n=-1
Now consider the line 0.5x−5y=9:
0.5x−5y=9
take -5y to the right side and 9 to the left side
0.5x-9=5y
switch sides
5y=0.5x-9
divide by 5
y=0.1x-9/5
so the slope of the line is m=0.1
let the slope of the line perpendicular to 0.5x−5y=9 be n, then
0.1*n=-1
n=-1/(0.1)=-10
Answer: -10