1) y + 8 = 0 means y = -8.
The graph is horizontal line parallel x-axis 8 units below x-axis.
2) x + 1 = 0 means x = -1.
The graph is vertical line parallel y-axis through the point x= -1.
Is there something in my response that you do not understand ?
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By the way, the response by tutor @Boreal is partly incorrect.
In his plot, the green line should be 1 unit to the left from the vertical ahis y.