Line c passes through the points (-3, -6) and (-1, -12). what is the slope of the line perpendicular to line c? a)-3 b)-1/3 c)1/3 d)3

Let's call the two points (x1,y1) and (x2,y2)

So that means (x1,y1) = (-3,-6) and (x2,y2) = (-1,-12)

Breaking things down further we can say
x1=-3
y1=-6
x2=-1
y2=-12

Plug those four values into the slope formula below and simplify
m = (y2 - y1)/(x2 - x1)
m = (-12 - (-6))/(-1 - (-3))
m = (-12 + 6)/(-1 + 3)
m = (-6)/(2)
m = -3

The slope of line C is -3 or -3/1



Take the fraction -3/1 and do two things to it

Step 1) Flip the fraction, or take the reciprocal, to get -3/1 > -1/3

Step 2) Flip the sign from negative to positive:  -1/3 > +1/3 = 1/3



The original slope is -3/1 and the perpendicular slope is 1/3

Final choice C, 1/3