x-intercept:

Substitute #color(red)(0)# for #color(red)(y)# in the equation and solve for #x#:

#color(red)(y) + 7 = -2x# becomes:

#color(red)(0) + 7 = -2x#

#7 = -2x#

#7/color(red)(-2) = (-2x)/color(red)(-2)#

#-7/2 = (color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2))#

#-7/2 = x#

#x = -7/2#

The x-intercept is #-7/2# or #(-7/2, 0)#

y-intercept:

Substitute #color(red)(0)# for #color(red)(x)# in the equation and solve for #y#:

#y + 7 = -2color(red)(x)# becomes:

#y + 7 = (-2 * color(red)(0))#

#y + 7 = 0#

#y + 7 - color(red)(7) = 0 - color(red)(7)#

#y + 0 = -7#

#y = -7#

The y-intercept is #-7# or #(0, -7)#