How to graph inequality on a plane

• Jun 29th 2010, 06:02 AM
OneidaFL
How to graph inequality on a plane
The part that gets me is the plane thing.

X + Y < 1

If x is 0 then Y is 0, -1, -2, -3 and so on right?

If y is 0 then the same applies for X =0, -1,-2, -3 and so on?

Please correct me if I am wrong.

Therefore How do I graph this? And what sets of numbers should I use?

00 for both won't work???
• Jun 29th 2010, 06:13 AM
HallsofIvy
Yes, the values you give are correct but the graph has to include non integers, rational and irrational numbers as well.

The graph of the equation, y= x+1, is a straight line. On that line, when x= 0, y= 1 and when y= 0, x= -1. The graph of y= x+1 is the straight line through (0, 1) and (-1, 0).

The reason you should graph that line first is that it forms the boundary of the points that satisfy y< x+ 1. Obviously that line divides all of $R^2$ into two subsets. The points that satisfy y< x+ 1 is one of the two subsets on either side of the line. Choose a point on each side of the line to determine which side satifies the inequality.

Also, because this is y< x+ 1, rather than $y\le x+1$, you don't want to include the line itself in the graph. One way to indicate that is to use a dashed line rather than a full line.