1. Sullivan Algebra and Trigonometry: Section 12.8
Objectives of this Section
Graph an Inequality
Graph a System of Linear Inequalities

2. An inequality in two variable x and y is satisfied by an ordered pair (a,b) if, when x is replaced by a and y by b, a true statement results.
A graph of an inequality in two variables x and y consists of all points (x,y) whose coordinates satisfy the inequality.

3. Steps For Graphing an Inequality
Step 1: Replace the inequality symbol with an equal sign and graph the resulting equation. If the inequality is strict, use dashes; if it is non-strict, use a solid line. This graph separates the xy-plane into two (or more) regions.
Step 2: In each of the regions, select a test point P.
a. If the coordinates of P satisfies the inequality, then so do all the points in the region. Indicate this by shading the region.
b. If the coordinates of P do not satisfy the inequality, then no points in the region do.

5. 2x - y -8 > 0 Test point: (1, 3) Test point: (5, 1)
2(1) = -9 < 0
Does not belong to graph
Test point: (5, 1)
2(5) = 1 > 0
Belongs to graph

6. y = 2x - 8 5
-10

7. Graph x - y = 6
y = x - 6
Graph 4x + 2y = 10
2y = -4x + 10
y = -2x + 5

8. y = x - 6
y = -2x + 5

9. Test Point: (0, 0)
x - y > 6
0 - 0 > 6 NO, shade side opposite (0, 0).
4x + 2y < 10
4(0) + 2(0) < 10 Yes, shade side containing (0, 0).

10. y < -2x + 5
y > x - 6