SOLUTION: I need to graph an inequality: y>-x The Solution book says the line runs through the origin and above, but I don't understand how to get the coordinate points. The book is Eleme

Algebra ->  Graphs -> SOLUTION: I need to graph an inequality: y>-x The Solution book says the line runs through the origin and above, but I don't understand how to get the coordinate points. The book is Eleme      Log On


   

Question 92502This question is from textbook Elementary Algebra
: I need to graph an inequality:
y>-x
The Solution book says the line runs through the origin and above, but I don't understand how to get the coordinate points.
The book is Elementary Algebra by Kaufmann & Schwitters
ISBN 0-495-10571-6
Chapter 8.2 pg. 339.
Thank you very much! This question is from textbook Elementary Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph y%3E-x, we need to graph the equation y=-x (just replace the inequality sign with an equal sign).
So lets graph the line y=-x (note: if you need help with graphing, check out this solver)
+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+-x%29+ graph of y=-x
Now lets pick a test point, say (0,1). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality y%3E-x with the test point

Substitute (0,1) into the inequality
%281%29%3E-%280%29 Plug in x=0 and y=1
1%3E0 Simplify




Since this inequality is true, we simply shade the entire region that contains (0,1)
Graph of y%3E-x with the boundary (which is the line y=-x in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)