In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2 , what is the slope of AB?
See attachment.

we have that
ABC is a right triangle
so
AB is perpendicular to BC
we know that
If two lines are perpendicular, then the product of their slopes is equal to [tex] -1 [/tex]
so
[tex] m1*m2=-1 [/tex]
in this problem
[tex] mAB*mBC=-1 [/tex]
solve for mAB
[tex] mAB=-\frac{1}{mBC} \\ \\ mAB=-\frac{1}{-\frac{1}{2}} \\ \\ mAB=2 [/tex]
therefore
the answer is
the slope of AB is equal to [tex] 2 [/tex]