Question

Line k passes through points (-3,-6) and (-1,12) what is the slope of the line perpendicular to line c

Answer 1

Do you mean "perpendicular to k"?  We have no line c there so I'm going with line k.  First we need the slope of line k.  Fitting those values into the slope formula we have $m= \frac{12-(-6)}{-1-(-3)} = \frac{18}{2} =9$.  So the slope of k is 9.  The slope of a line perpendicular to k has the opposite sign and the fraction is flipped.  The perpendicular slope then is -1/9.