[mother74]

how to graph y<2x+2

[ArcSine]

Start by graphing the equality y = 2x + 2.

Now, all the points which satisfy your inequality will be those points lying on one side of the line or the other. The inequality's graph is commonly indicated by shading all of the graph on the appropriate side of the line.

Since you have a strict inequality, the line y = 2x + 2 is not part of the solution set, so indicate this by drawing the line as a dashed line, rather than solid.

As to which side of the line to shade, it'll usually be pretty intuitive when you think about whether the qualifying values of y must be greater than, or less than, that value of y which satisfies the equality. But whether you take the intuitive approach or not, it's a good idea to check yourself by picking a 'test point' on either side of the line (the point (0, 0) is an easy choice, unless the line passes through the origin). If the chosen test point satisfies the inequality, then you shade the side of the line which contains the test point. If the test point fails the inequality, shade the other side.