To find the x-intercept:
Substitute #0# for #y# and solve for #x#:
#1/2x + 2y = -2# becomes:
#1/2x + (2 * 0) = -2#
#1/2x + 0 = -2#
#1/2x = -2#
#color(red)(2) * 1/2x = color(red)(2) * -2#
#cancel(color(red)(2)) * 1/color(red)(cancel(color(black)(2)))x = -4#
#x = -4#
The x-intercept is #x =-4# or #(-4, 0)#
To find the y-intercept:
Substitute #0# for #x# and solve for #y#:
#1/2x + 2y = -2# becomes:
#(1/2 * 0) + 2y = -2#
#0 + 2y = -2#
#2y = -2#
#(2y)/color(red)(2) = -2/color(red)(2)#
#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = -2/color(red)(2)#
#y = -1#
The y-intercept is #y =-1# or #(0, -1)#