Graphing Systems of Inequalities
Key Questions

A linear inequality is in the form:
#ax + by > c# or ax + by < c.First, graph the line ax + by  c = 0 by the 2 yintercepts and xintercepts.
Then find the area (above or below the line) that make the inequality true. You may use the origin O (0, 0) as test point
Example. Solve: 2x + 3y > 4
First, graph the line 2x + 3y + 4 = 0 by the 2 x and y intercepts.
Make x = 0 > 3y = 4 > y = 4/3
Make y = 0 > 2x = 4 > x = 2
Solve the inequality: f(x) = 2x + 3y + 4 > 0 by using origin O (0, 0) as test point. We get 4 > 0, It is true, then the area above the line is the solution set.
graph{2x + 3y + 4 = 0 [10, 10, 5, 5]} 
By linear inequality in one variable, do you mean something like
#x <= 5# or
#y > 2# If yes, just draw your line and shade the entire area that satisfies your inequality
For example, in
#x <= 5# ,
we should draw a vertical line at#x = 5# and shade the entire area to its left (since#<=# )For y > 2, we should draw a broken horizontal line (since
#># , not#>=# ) at y = 2 and shade the entire area above it