\(\displaystyle x+y>2\)
\(\displaystyle y>2-x\)
Since y is always on the vertical axis,
unless you're like me and "cheat" when graphing inverses,
then the region above the line
\(\displaystyle y=2-x\)
contains all values of \(\displaystyle y>2-x\)
since y=2-x on the line, y<2-x below the line and y>2-x above the line.
\(\displaystyle 3x-2y<k\)
\(\displaystyle 3x<2y+k\)
\(\displaystyle 3x-k<2y\)
\(\displaystyle y>\frac{3}{2}x-\frac{k}{2}\)
Same story, just fill in the blank for k.
The equations you specified are "linear", straight lines.
Hence the inequalities are relatively easy.
I also recommend you do what Mark asked,
otherwise I messed up his post.