how do I graph this inequality y<2x+2

Graph the line, Y=2X+2.
Figure out which area (above or below the line) is included when Y < 2X+2

Note that the inequality sign is "<", so the area does not include the line.

First, plot the graph y=2x+2 and you are done. With this line, you have divided the plane into two parts. Everywhere on one side of the line y > 2x+2; on the line y = 2x+2; everywhere on the other side of the line y < 2x+2. What you have left is to find for which side of the two y < 2x+2. Hint: just pick a random point in one of the sides, let's say (x,y)=(0,0), or (1,1), which are below the line y=2x+2, and see if they satisfy or do not satisfy your inequality. Then try the other side and then pick one side on which the point satisfy the inequality.

Graph the inequality
y < 2x + 2