Question 303594: What is the correct graph inequalities of x + y < 4?
Answer by graphmatics(170)   (Show Source):
You can put this solution on YOUR website! First consider the graph of x+y = 4. You should put it in the y = mx+b form, so y = -x+4. Graph the equation, so place x = 4 and get y = 4 so (0,4) is the y intercept of this linear equation. Next put y = 0 and get x = 4 so (4,0) is the x intercept of the linear equation. the graph of the linear system is a line passing through these two points. This line when graphed divides the xy plane in three parts, the part where the line is or x+y=4, the part where x+y > 4 and the part we want x+y < 4. Check the validity of the inequality for the left and right side of the line . If you check the left side you will find (0,0) is a point on the left side and 0+0 is less than 4 so the left side fulfill the inequality. To check the right side note that (5,0) is a point on the right side and that 5+0 is greater than 4. So the solution is the left side not including the line.
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