Question

an equation of a line perpendicular to the line represented by the equation y=-1:2x-5 and passing through (6,-4) is

Answer 1

Whatever you intended to type before the 'x' . . . " -1.2 "  or  " - 1/2 " . . .
that's the slope of the line represented by the equation.

A line perpendicular to it has a slope with the negative reciprocal of this one.
So the perpendicular line would be

       y = 0.8333 x  (negative reciprocal of  -1.2)  +  any number
or
       y = 2 x  (negative reciprocal of  - 1/2)  +  any number