To sketch the graph of
y<-3/2x + 3
we need to draw the line:
y = -3/2x + 3
Substituting x = 0:
y = -3/2(0) + 3
y = 3
Substituting y = 0:
0 = -3/2x + 3
-3 = -3/2x
-3*(-2/3) = x
2 = x
Then, the line (which is a dashed line because the points on the line are not a solution to the inequality) passes through (0, 3) and (2, 0)
Now, we have to find if a point is a solution or not. Replacing with (0,0) into the inequality:
0 < -3/2(0) + 3
0 < 3
which is correct, then we need to shade the side that includes (0,0)