Question 355462
The slope of the line pasing through (4,-6) and (3, -4) is
{{{(-4-(-6))/(3-4) = 2/(-1)= -2}}}.  The slope of the line perpendicular to this is equal to its negative reciprocal:  1/2.  Therefore the equation of the line with slope 1/2 and passing through (6,-10) is 
{{{y-(-10) = (1/2)(x-6)}}}, or
{{{y + 10 = (1/2)(x-6)}}},
{{{y = (1/2)x-3-10}}},
{{{y = (1/2)x-13}}}.