If put into slope intercept form...y=mx+b where m=slope
8x+9y=1
9y=-8x+1
y=(-8x+1)/9
So the slope is -8/9
For a line to be perpendicular to this one, it must have the negative reciprocal slope of the reference line:
Mathematically, for two lines to be perpendicular to each other:
m1*m2=-1 in this case:
-8m/9=-1
m=-9/-8
m=9/8 or if you prefer
m=1.125
For your curiosity...since slope equals dy/dx we can say that:
tanα=(dy/dx) and in this context
tanα=m so the angle is:
α=arctan(m)
a=arctan(-8/9)≈-41.63
b=arctan(9/8)≈48.37
So the difference between b and a is 48.37--41.63=90° Since they are at a 90° to each other, they are perpendicular...
