For lines to be perpendicular to one another the product of their slopes must be negative one. Or in other words their slopes must be negative reciprocals of one another. Mathematically this is:
m1*m2=-1, in this case our reference lines is:
0.5x-5y=9
5y=0.5x-9
y=0.1x-1.8 so its slope is 0.1, so the perpendicular slope, m, is:
0.1m=-1
m=-10
So the slope of the line perpendicular to 0.5x-5y=9 is -10.
