the same principles apply with these as in your other thread about graphing inequalities, in that, we will attempt to solve the inequalities in such a way that they look like formulas we recognize.

1)

x + y < 1

let's solve for y

=> y < -x + 1

hmm, if not for the inequality sign,this would look like a line, with slope -1 and y intercept 1, and that's what we will draw. however, since it is an inequality, we have to shade the region where y is less than the values given by the line. the line is not included in the solution since we have a strictly less than sign, so we must draw a broken line. see below