Download presentation

Presentation is loading. Please wait.

Published byMelvyn Sims Modified over 4 years ago

1
3.3 Linear Inequalities in Two Variables Objectives: Solve and graph a linear inequality in two variables. Use a linear inequality in two variables to solve real-world problems. Standard: 2.8.11.K. Apply an appropriate technique to graph a linear inequality.

2
A linear inequality in two variables, x and y, is any inequality that can be written in one of the forms below, where A ≠ 0 and B ≠ 0. Ax + By ≥ C Ax + By > C Ax + By ≤ C Ax + By C Ax + By ≤ C Ax + By < C

3
A solution of a linear inequality in two variables, x and y, is an ordered pair (x, y) that satisfies the inequality. The solution to a linear inequality is a region of the coordinate plane and is called a half-plane bounded by a boundary line.

4
Graphing Linear Inequalities 1. Given a linear inequality in two variables, graph its related linear equation. For inequalities involving ≤ or ≥, use a solid boundary line. For inequalities involving ≤ or ≥, use a solid boundary line. For inequalities involving, use a dashed boundary line. For inequalities involving, use a dashed boundary line.

5
2. Shade the appropriate region. For inequalities in the form of y ≤ mx + b or For inequalities in the form of y ≤ mx + b or y < mx + b, shade below the boundary line. y < mx + b, shade below the boundary line. For inequalities of the form y ≥ mx + b or For inequalities of the form y ≥ mx + b or y > mx + b, shade above the boundary line. y > mx + b, shade above the boundary line. For inequalities in the form x ≤ c or x < c, shade to the left of the boundary line. For inequalities in the form x ≤ c or x < c, shade to the left of the boundary line. For inequalities in the form x ≥ c or x > c, shade to the right of the boundary line. For inequalities in the form x ≥ c or x > c, shade to the right of the boundary line.

6
Ex 1. Graph each linear inequality. a. y < x + 2 a. y < x + 2

7
b. y ≥ -2x + 3

8
* c. y > -2x - 2 Dotted Line

9
d. y ≥ 2x + 5

10
e. -2x –3y ≤ 3

11
f. 3x – 4y ≥ 4 -4y≥-3x + 4 y ≤ ¾ x - 1

12
g. -5x – 2y > 4 g. -5x – 2y > 4 -2y > 5x + 4 y < -5/2 x - 2 Dotted Line

14
Ex 3. Graph each linear inequality. x is a vertical line and y is a horizontal line

15
a. x > -2

16
b. y ≤ -1

17
c. x ≤ -2 c. x ≤ -2

18
d. y > -1 Dotted Line

19
Writing Activities

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google