first find the slope
the slope of the line that passes through (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
given
(-4,3) and (6,-2)
the slope is (-2-3)/(6-(-4))=(-5)/(6+4)=-5/10=-1/2
so
the equation of a line tat passes through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
use (-4,3)
and we found slope=-1/2
y-3=-1/2(x-(-4))
y-3=-1/2(x+4)
if yo want slope intercept form
y-3=-1/2x-2
y=-1/2x+1
if yo want standard form
1/2x+y=1
x+2y=2