Question

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

Answer 1

The slope of AB is 2. 
Segmet AB is perpendicular to segment BC, and the slope of the perpendicular line  (segment AB) is the negative reciprocal of the slope of the original or reference line (segment BC). The negative reciprocal of -1/2 is 2. Hope this helps. 

Answer 2

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 $-1$

so

$m1*m2=-1$

in this problem

$mAB*mBC=-1$

solve for mAB

$mAB=-\frac{1}{mBC} \\ \\ mAB=-\frac{1}{-\frac{1}{2}} \\ \\ mAB=2$

therefore

the answer is

the slope of AB is equal to $2$