If two lines are parallel they have the same slope. Since both of these equations are in slope intercept format, y=mx+b, it is easy to see the slope. It is the coefficient of the x, or m. What is the slope of the first line? It is the coefficient of x, which is 1. What is the slope of the second line? It is the coefficient of x, which is -1. The lines do not have the same slope so they are not parallel.
Perpendicular lines have slopes that are the negative reciprocal of each other. So if one line has a slope of 3, the line perpendicular to it has a slope of -1/3. 1 and -1 are the negative reciprocal of each other so these lines are perpendicular to each other.