To determine which half-plane to shade, pick a test point that is not on the boundary. Check whether that point satisfies the inequality. If it does, shade the half-plane that includes the test point. If not, shade the other half-plane. The origin, (0, 0), is usually an easy test point as long as it is not on the boundary.
Problem 1 Graphing Linear Inequalities
What is the graph of each inequality?
-
-
Step 1
Graph the boundary line
-
Step 2
Choose a test point, (0, 0). Substitute
Since
-
-
The boundary line is again
Shade the region opposite the region shaded above (for
You can also check the point (0, 0).
Since
Plan
Can you use the graph of
If you shaded above the line for
✓ Got It?
- What is the graph of each inequality?
-
You can also inspect inequalities solved for y, such as
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions