Page 662 - Algebra 1

L E S S O N Graphing Linear Inequalities 97
Warm Up
1. Vocabulary The of the equation of a line is y = mx + b, where (49) m is the slope of the line and b is the y-intercept.
Determine the slope and the y-intercept of each equation. 2. y=-_1x-5 3. 2x+2y=6
(49) 3 (49)
Graph each of the following inequalities on a number line.
New Concepts
4. y < 3 5. x ≥ -2 (50) (50)
A linear inequality is similar to a linear equation, except that a linear inequality has an inequality symbol instead of an equal sign. A solution of a linear inequality is any ordered pair that makes the inequality true.
You can evaluate an inequality with an ordered pair to find out if the ordered pair makes the inequality true and is a solution.
Determining Solutions of Inequalities
Determine if each ordered pair is a solution of the given inequality.
a. (0, 4); y > 5x - 1 SOLUTION
y > 5x -1
4 > 5(0) -1 Evaluate the inequality for the point (0, 4). 4 > -1 Simplify.
The inequality is true. The ordered pair (0, 4) is a solution.
b. (3,-3);y<-3x+6 SOLUTION
y < -3x + 6
-3 < -3(3) + 6 Evaluate the inequality for the point (3, -3).
-3 < -3 Simplify.
The inequality is not true because -3 is not less than -3. The ordered pair (3, -3) is not a solution.
c. (-4, 8); y ≤ 9 SOLUTION
y≤9
8 ≤ 9 Evaluate the inequality for the point (-4, 8). The inequality is true. The ordered pair (-4, 8) is a solution.
Example
1
Hint
The inequalities y ≤ 9 and y ≤ 0x + 9 are equivalent. If an ordered pair is a solution of the inequality, then the y-coordinate is less than or equal to 9, and the x-coordinate can be any real number.
Online Connection www.SaxonMathResources.com
Lesson 97 647